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SLIDE 1
Four colleagues go on a business trip together. Their costs are £1,580 for four return plane tickets, £740 to rent an apartment, £320 to hire a car. What is the cost per colleague for the journey?
SLIDE 2
Four colleagues go on a business trip together. Their costs are £1,580 for four return plane tickets, £740 to rent an apartment, £320 to hire a car. What is the cost per colleague for the journey?
The total cost is £2640. When this is divided between four people the cost per person is £660.
SLIDE 1B
Four colleagues go on a business trip together. Their costs are $1,580 for four return plane tickets, $740 to rent an apartment, $320 to hire a car. What is the cost per colleague for the journey?
SLIDE 2B
Four colleagues go on a business trip together. Their costs are $1,580 for four return plane tickets, $740 to rent an apartment, $320 to hire a car. What is the cost per colleague for the journey?
The total cost is $2640. When this is divided between four people the cost per person is $660.
?
?
SLIDE 3
The cost of 1 tin of jam is £3.50. What is the cost of 8 tins?
SLIDE 4
The cost of 1 tin of jam is £3.50. What is the cost of 8 tins?
Solution
Answer: £28
SLIDE 3
The cost of 1 tin of jam is $3.50. What is the cost of 8 tins?
SLIDE 4
The cost of 1 tin of jam is $3.50. What is the cost of 8 tins?
Solution
Answer: $28
SLIDE 5
Paying by instalments
A typical way in which people buy a good is to pay a fixed sum over a period. Each fixed payment is called an instalment. Often the purchaser has to make a first down payment, also called a deposit. Buying a good like this is a way to taking out a loan. A loan company lends the purchaser the money, and the total paid is greater than the original price. The loan company makes a profit by charging interest.
Question
The total cost of a family holiday was £4,200 plus sales tax of £840. The family paid a deposit of £1,200. The rest of the money was paid in 6 equal monthly instalments. Work out the amount of each monthly payment.
SLIDE 6
The total cost of a family holiday was 4,200 plus sales tax of £840. The family paid a deposit of £1,200. The rest of the money was paid in 6 equal monthly instalments. Work out the amount of each monthly payment.
Solution
Answer: £640
Notes for tutors
Here we see a theme of language across the curriculum. A practical problem arises in the world, and involves new ideas such as loan, profit, deposit and instalment. The student not only needs to understand the mathematical solution but needs to understand the practical context. That goes together with an expansion of vocabulary sufficient to describe the real-life problem.
Paying by instalments
A typical way in which people buy a good is to pay a fixed sum over a period. Each fixed payment is called an instalment. Often the purchaser has to make a first down payment, also called a deposit. Buying a good like this is a way to taking out a loan. A loan company lends the purchaser the money, and the total paid is greater than the original price. The loan company makes a profit by charging interest.
SLIDE 5b
Paying by instalments
A typical way in which people buy a good is to pay a fixed sum over a period. Each fixed payment is called an instalment. Often the purchaser has to make a first down payment, also called a deposit. Buying a good like this is a way to taking out a loan. A loan company lends the purchaser the money, and the total paid is greater than the original price. The loan company makes a profit by charging interest.
Question
The total cost of a family holiday was $4,200 plus sales tax of $840. The family paid a deposit of $1,200. The rest of the money was paid in 6 equal monthly instalments. Work out the amount of each monthly payment.
SLIDE 6b
The total cost of a family holiday was $4,200 plus sales tax of $840. The family paid a deposit of $1,200. The rest of the money was paid in 6 equal monthly instalments. Work out the amount of each monthly payment.
Solution
Answer: $640
SLIDE 7
Mr. Read wishes to travel to Alaska with his wife and daughter aged 10. They have $1600 dollars to spend. The table shows prices of flights on selected days.
Outward flight Return flight
Date Adult ticket ($) Date Adult ticket ($)
3 June 300 15 June 310
4 June 320 16 June 400
5 June 280 17 June 350
6 June 280 18 June 310
Flights for children below 16 are half of the price of the adult ticket.
? Can Mr. Read afford to travel out on 3 June and return on 17 June?
? What is the option Mr. Read can afford that gives him the most time in Alaska?
SLIDE 8
Mr. Read wishes to travel to Alaska with his wife and daughter aged 10. They have $1600 dollars to spend. The table shows prices of flights on selected days.
Outward flight Return flight
Date Adult ticket ($) Date Adult ticket ($)
3 June 300 15 June 310
4 June 320 16 June 400
5 June 280 17 June 350
6 June 280 18 June 310
Flights for children below 16 are half of the price of the adult ticket.
Solution
? Can Mr. Read afford to travel out on 3 June and return on 17 June?
3 June:
17 June:
too expensive
? What is the option Mr. Read can afford that gives him the most time in Alaska?
5 June:
18 June:
3 June to 18 June costs $1525 and is also affordable, but the 5 June to 18 June option is the best.
SLIDE 9
A shop sells mayonnaise in three different sizes.
200 ml costs £4.
300 ml costs £5.40
400 ml costs £7.60
Which size is best value for money?
SLIDE 10
A shop sells mayonnaise in three different sizes.
200 ml costs £4.
300 ml costs £5.40
400 ml costs £7.60
Which size is best value for money?
Solution
Cost per 100 ml.
Answer: 300 ml for £5.40
SLIDE 9 B
A shop sells mayonnaise in three different sizes.
8 fl. oz. costs $4.
12 fl. oz. costs $5.40
16 fl. oz. costs $7.60
Which size is best value for money?
SLIDE 10 B
A shop sells mayonnaise in three different sizes.
8 fl. oz. costs $4.
12 fl. oz. costs $5.40
16 fl. oz. costs $7.60
Which size is best value for money?
Solution
Cost per fluid once.
Answer: 12 fl. oz. for $5.40
SLIDE 11
Oil is sold in two sizes. A 1.6 litre bottle normally costs £10. A 6.4 litre bottle costs £35. A shop is offering a reduction of one tenth on a purchase of two or more 1.6 litre bottles. Is it cheaper to buy the 6.4 litre bottle, or four 1.6 litre bottles?
SLIDE 12
Oil is sold in two sizes. A 1.6 litre bottle normally costs £10. A 6.4 litre bottle costs £35. A shop is offering a reduction of one tenth on a purchase of two or more 1.6 litre bottles. Is it cheaper to buy the 6.4 litre bottle, or four 1.6 litre bottles?
Solution
Reduction of one tenth is £4
But it is still cheaper to buy the 6.4 litre bottle at £35.
SLIDE 11B
Oil is sold in two sizes. A 1.6 pint bottle normally costs $10. A 6.4 pint bottle costs $35. A shop is offering a reduction of one tenth on a purchase of two or more 1.6 pint bottles. Is it cheaper to buy the 6.4 pint bottle, or four 1.6 pint bottles?
SLIDE 12B
Oil is sold in two sizes. A 1.6 pint bottle normally costs $10. A 6.4 pint bottle costs $35. A shop is offering a reduction of one tenth on a purchase of two or more 1.6 pint bottles. Is it cheaper to buy the 6.4 pint bottle, or four 1.6 pint bottles?
Solution
Reduction of one tenth is $4
But it is still cheaper to buy the 6.4 pint bottle at £35.
SLIDE 13
Two dealers make an offer on their used cars.
Dealer A. Sale price. 1/5 off the price of any car up to £2,200.
Dealer B. Sale price. 1/4 off the price of any car normally priced over £1,800.
A special offer is made by both dealers: If the sale price is over £1,800, then take another tenth off.
Is a car normally priced at £2000 at Dealer A cheaper than a car normally priced at £2,500 at Dealer B?
SLIDE 14
Two dealers make an offer on their used cars.
Dealer A. Sale price. 1/5 off the price of any car up to £2,200.
Dealer B. Sale price. 1/4 off the price of any car normally priced over £1,800.
A special offer is made by both dealers: If the sale price is over £1,800, then take another tenth off.
Is a car normally priced at £2000 at Dealer A cheaper than a car normally priced at £2,500 at Dealer B?
Solution
Dealer A: 1/5 is £400.
No further reduction
Dealer B: 1/4 of £2500 is £625
A further tenth is £187.5
Dealer A is cheaper.
SLIDE 13B
Two dealers make an offer on their used cars.
Dealer A. Sale price. 1/5 off the price of any car up to $2,200.
Dealer B. Sale price. 1/4 off the price of any car normally priced over $1,800.
A special offer is made by both dealers: If the sale price is over $1,800, then take another tenth off.
Is a car normally priced at $2000 at Dealer A cheaper than a car normally priced at $2,500 at Dealer B?
SLIDE 14B
Two dealers make an offer on their used cars.
Dealer A. Sale price. 1/5 off the price of any car up to $2,200.
Dealer B. Sale price. 1/4 off the price of any car normally priced over $1,800.
A special offer is made by both dealers: If the sale price is over $1,800, then take another tenth off.
Is a car normally priced at $2000 at Dealer A cheaper than a car normally priced at $2,500 at Dealer B?
Solution
Dealer A: 1/5 is $400.
No further reduction
Dealer B: 1/4 of $2500 is $625
A further tenth is $187.5
Dealer A is cheaper.
SLIDE 15
A metal frame is made from wire.
The height of the frame is 1 metre and the width 3 metres. The weight of the metal is 4 kg per metre. What is the weight in kg of the metal in the frame?
SLIDE 16
A metal frame is made from wire.
The height of the frame is 1 metre and the width 3 metres. The weight of the metal is 4 kg per metre. What is the weight in kg of the metal in the frame?
Solution
Total length metres
Total weight kg
SLIDE 15B
A metal frame is made from wire.
The height of the frame is 1 yard and the width 3 yards. The weight of the metal is 4 lb per metre. What is the weight in lb of the metal in the frame?
SLIDE 16B
A metal frame is made from wire.
The height of the frame is 1 metre and the width 3 metres. The weight of the metal is 4 kg per metre. What is the weight in kg of the metal in the frame?
Solution
Total length yards
Total weight lb
SLIDE 17
A farmer wishes to build a fence around a field, which has a diameter of 1400 m.
The length of the semicircular part is 2200 m. It costs £50 for each 100 m of fence and will take 3 days to build. The cost of each day of work is £180 per day. What is the total cost of building the fence?
SLIDE 18
A farmer wishes to build a fence around a field, which has a diameter of 1400 m.
The length of the semicircular part is 2200 m. It costs £50 for each 100 m of fence and will take 3 days to build. The cost of each day of work is £180 per day. What is the total cost of building the fence?
Solution
Total length:
Cost of labour:
Total cost:
SLIDE 17B
A farmer wishes to build a fence around a field, which has a diameter of 1400 yd.
The length of the semicircular part is 2200 yd. It costs $50 for each 100 yd of fence and will take 3 days to build. The cost of each day of work is $180 per day. What is the total cost of building the fence?
SLIDE 18B
Solution
Total length:
SLIDE 19
A gardener wishes to put a plastic strip around the edge of a flower bed, which is a circle with circumference 22 m. The plastic strip is sold in rolls of 6 m. How many rolls of plastic strip will the gardener need to buy?
SLIDE 20
A gardener wishes to put a plastic strip around the edge of a flower bed, which is a circle with circumference 22 m. The plastic strip is sold in rolls of 6 m. How many rolls of plastic strip will the gardener need to buy?
Solution
4 rolls needed, with 2 m left over.
SLIDE 19B
A gardener wishes to put a plastic strip around the edge of a flower bed, which is a circle with circumference 22 yd. The plastic strip is sold in rolls of 6 yd. How many rolls of plastic strip will the gardener need to buy?
SLIDE 20B
A gardener wishes to put a plastic strip around the edge of a flower bed, which is a circle with circumference 22 yd. The plastic strip is sold in rolls of 6 yd. How many rolls of plastic strip will the gardener need to buy?
Solution
4 rolls needed, with 2 yd left over.
SLIDE 21
The table gives the rates of pay of a shop assistant.
Day Rate of pay
Monday to Friday £9.60 per hour
Weekend £12.20 per hour
The assistant worked 35 hours in a week, of which 12 were at the weekend. Her rent is £150 dollars a week. How much did she have at the end of the week after she had paid the rent?
SLIDE 22
The table gives the rates of pay of a shop assistant.
Day Rate of pay
Monday to Friday £9.60 per hour
Weekend £12.20 per hour
The assistant worked 35 hours in a week, of which 12 were at the weekend. Her rent is £150 dollars a week. How much did she have at the end of the week after she had paid the rent?
Solution
hours at the basic rate
Monday to Friday
Weekend
Total pay
Net after rent
SLIDE 21B
The table gives the rates of pay of a shop assistant.
Day Rate of pay
Monday to Friday $9.60 per hour
Weekend $12.20 per hour
The assistant worked 35 hours in a week, of which 12 were at the weekend. Her rent is $150 dollars a week. How much did she have at the end of the week after she had paid the rent?
SLIDE 22B
Solution
hours at the basic rate
Monday to Friday
Weekend
Total pay
Net after rent
SLIDE 23
What is the total cost of six pens for 80p, fifteen pencils at 40p, four rulers at £1.25 and eight exercise books at £2.15?
SLIDE 24
What is the total cost of six pens for 80p, fifteen pencils at 40p, four rulers at £1.25 and eight exercise books at £2.15?
Solution
Total cost:
SLIDE 23B
What is the total cost of six pens for 80¢, fifteen pencils at 40¢, four rulers at $1.25 and eight exercise books at $2.15?
SLIDE 24B
What is the total cost of six pens for 80¢, fifteen pencils at 40¢, four rulers at $1.25 and eight exercise books at $2.15?
Solution
Total cost:
SLIDE 25
A young girl decides to make money by selling sweets to her friends. She buys 10 kg of sweets for £24. She buys sufficient little boxes for £2. She divides the sweets into 250g amounts and puts each of these amounts into the boxes. She sells each box for 95p. Assuming she has no boxes left over, what profit did she make?
Hint
250g is ¼ of a kilo, so there are 4 times 250g in 1 kg.
SLIDE 26
A young girl decides to make money by selling sweets to her friends. She buys 10 kg of sweets for £24. She buys sufficient little boxes for £2. She divides the sweets into 250g amounts and puts each of these amounts into the boxes. She sells each box for 95p. Assuming she has no boxes left over, what profit did she make?
Hint
250g is ¼ of a kilo, so there are 4 times 250g in 1 kg.
Solution
Costs
Number of sales
Revenue
Profit
SLIDE 25B
A young girl decides to make money by selling sweets to her friends. She buys 10 lb of sweets for $24. She buys sufficient little boxes for $2. She divides the sweets into 4oz amounts and puts each of these amounts into the boxes. She sells each box for 95¢. Assuming she has no boxes left over, what profit did she make?
Hint
4 oz is ¼ of a pound, so there are 4 times 4 oz in 1 lb.
SLIDE 26B
Solution
Costs
Number of sales
Revenue
Profit
SLIDE 27
The same young girl decides to expand her business. She buys 1000 kg of sweets for £1,900. She buys sufficient boxes for £60. She pays a boy to pack the boxes containing 250g of sweets, giving him a wage of £8 per hour. She sells each box for 95p. He packs 50 boxes per hour. What is her profit?
250g is ¼ of a kilo, so there are 4 times 250g in 1 kg.
SLIDE 28
The same young girl decides to expand her business. She buys 1000 kg of sweets for £1,900. She buys sufficient boxes for £60. She pays a boy to pack the boxes containing 250g of sweets, giving him a wage of £8 per hour. She sells each box for 95p. He packs 50 boxes per hour. What is her profit?
250g is ¼ of a kilo, so there are 4 times 250g in 1 kg.
Solution
Number of sales
Hours worked
Wage costs
Costs
Revenue
Profit
SLIDE 27B
The same young girl decides to expand her business. She buys 1000 lb of sweets for $1,900. She buys sufficient boxes for $60. She pays a boy to pack the boxes containing 4 oz of sweets, giving him a wage of $8 per hour. She sells each box for 95¢. He packs 50 boxes per hour. What is her profit?
SLIDE 28B
Solution
Number of sales
Hours worked
Wage costs
Costs
Revenue
Profit
SLIDE 29
The same young girl decides to expand her business a second time. She buys 10,000 kg of sweets for £15,000. She buys sufficient boxes for £600. She pays several boys to pack the boxes each containing 250g of sweets, giving them a wage of £8 per hour. They pack the boxes at 50 per hour. She sells the sweets for 95p per box.
The government gets wind of her business and imposes a social security payment of £1 per hour worked by the boys; then a 4/10 tax on her profits before social security is taken off, and a fine of £20,000 for not declaring her turnover. Calculate her net profit or loss after tax and all deductions.
Turnover is another word for sales or revenue. It is the amount of money taken by a business in a period.
SLIDE 30
The same young girl decides to expand her business a second time. She buys 10,000 kg of sweets for £15,000. She buys sufficient boxes for £600. She pays several boys to pack the boxes each containing 250g of sweets, giving them a wage of £8 per hour. They pack the boxes at 50 per hour. She sells the sweets for 95p per box.
The government gets wind of her business and imposes a social security payment of £1 per hour worked by the boys; then a 4/10 tax on her profits before social security is taken off, and a fine of £20,000 for not declaring her turnover. Calculate her net profit or loss after tax and all deductions.
Solution
Number of sales
Hours worked
Wage costs
Costs
Revenue
Profit before charges
Tax: £6,400, Social security: £800, Fine: £20,000
Charges
Net loss
SLIDE 29B
The same young girl decides to expand her business a second time. She buys 10,000 lb of sweets for $15,000. She buys sufficient boxes for $600. She pays several boys to pack the boxes each containing 4 oz of sweets, giving them a wage of $8 per hour. They pack the boxes at 50 per hour. She sells the sweets for 95¢ per box.
The government gets wind of her business and imposes a social insurance payment of $1 per hour worked by the boys; then a 4/10 tax on her profits before social insurance is taken off, and a fine of $20,000 for not declaring her turnover. Calculate her net profit or loss after tax and all deductions.
Turnover is another word for sales or revenue. It is the amount of money taken by a business in a period.
SLIDE 30B
Solution
Number of sales
Hours worked
Wage costs
Costs
Revenue
Profit before charges
Tax: $6,400, Social insurance: $800, Fine: $20,000
Charges
Net loss
SLIDE 31
Speedy Deliveries buy a van for £16,500 plus sales tax of £3,300. They make a down-payment for the van of £4,200. They pay the balance in 12 equal instalments. How much is each instalment?
A down-payment is an initial payment for a purchase. The rest of the purchase is bought on credit and paid for in instalments.
SLIDE 32
Speedy Deliveries buy a van for £16,500 plus sales tax of £3,300. They make a down-payment for the van of £4,200. They pay the balance in 12 equal instalments. How much is each instalment?
Solution
Each instalment is £1,300
SLIDE 31B
Speedy Deliveries buy a van for $16,500 plus sales tax of $3,300. They make a down-payment for the van of $4,200. They pay the balance in 12 equal instalments. How much is each instalment?
A down-payment is an initial payment for a purchase. The rest of the purchase is bought on credit and paid for in instalments.
SLIDE 32B
Solution
Each instalment is $1,300
SLIDE 33
A High School puts on a production of West Side Story. They charge admission. The expenses of the production are £1,300. When 300 tickets were sold, the School made a profit of £1,700. What will be the profit in a second similar production if 450 tickets are sold, assuming the same costs?
SLIDE 34
A High School puts on a production of West Side Story. They charge admission. The expenses of the production are £1,300. When 300 tickets were sold, the School made a profit of £1,700. What will be the profit in a second similar production if 450 tickets are sold, assuming the same costs?
Solution
Costs
per ticket
Sales of second production
Profit of second production
SLIDE 33B
A High School puts on a production of West Side Story. They charge admission. The expenses of the production are $1,300. When 300 tickets were sold, the School made a profit of $1,700. What will be the profit in a second similar production if 450 tickets are sold, assuming the same costs?
SLIDE 34B
Solution
Costs
Sales of second production
Profit of second production
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