High School Maths · Year 2 · Unit 14 · Lesson 5 of 5

Exchange Rates and Best Buys: Get the Most for Your Money

About 15 minutes · changing money both ways with a given exchange rate · commission on exchange · changing money back · finding the rate · unit prices and best buys · special offers · money to the nearest cent · calculator allowed · exit quiz

Hook

At an airport, booth A offers 1 dollar = 0.8 euros but takes 5% of the euros as commission. Booth B offers 1 dollar = 0.77 euros with no commission.

You want to change $500. Which booth gives you more euros?

Booth B. Booth A: 500 × 0.8 = 400 euros, minus 5% commission (20 euros) = 380 euros. Booth B: 500 × 0.77 = 385 euros. The better-looking rate is not always the better deal. (The rates in this lesson are made up for practice. Real rates change every day.)

Learn

Master the essentials

Exchange rate

Says how much of one currency you get for one unit of another. Always use the rate given in the question.

With 1 dollar = 0.8 euros: $50 = 40 euros

Dollars to the other currency

Multiply by the rate.

$250 × 0.8 = 200 euros

Back to dollars

Divide by the rate.

300 euros ÷ 0.8 = $375

Check the size

Here 1 dollar buys less than 1 euro, so you get fewer euros than dollars. If the answer goes the wrong way, you multiplied instead of dividing.

$250 → 200 euros (fewer)

Commission

A fee taken by the exchange service, often a percentage. Take it off the amount it is charged on.

2% of $600 = $12, so $588 is changed

Unit price

Price ÷ amount. The lower unit price is the better buy.

$3.60 for 450 g: 0.8 cents per g

Same amount

Or find the cost of the same amount of each, such as 100 g or 1 litre.

1 litre for $2.40, or 750 ml for $1.71: $2.40 against $2.28 a litre

Offers

"3 for 2" means you get 3 items but pay for 2. Find the cost of one item.

3 for 2 at $4.50 each: $9 ÷ 3 = $3

Worked examples

See it done

1. Use the rate 1 dollar = 0.78 pounds. (a) Change $640 into pounds. (b) Change 273 pounds into dollars.

  1. (a) Dollars to pounds: multiply. 640 × 0.78 = 499.20 pounds.
  2. (b) Pounds to dollars: divide. 273 ÷ 0.78 = $350.
  3. Check: 1 dollar buys less than 1 pound, so the number of pounds is always smaller ✓.

(a) 499.20 pounds (b) $350

2. Ivy changes $1,200 into euros. Use the rate 1 dollar = 0.92 euros. The booth takes 1.5% commission from the dollars before changing them. How many euros does she get?

  1. Commission: 1.5% of 1,200 = $18.
  2. Dollars changed: 1,200 − 18 = $1,182. (Or 1,200 × 0.985.)
  3. Euros: 1,182 × 0.92 = 1,087.44 euros.

1,087.44 euros

3. Orange juice is sold in three bottle sizes: 500 ml for $1.85, 1.5 litres for $5.10, and 750 ml for $2.70. Which bottle is the best buy?

  1. Compare the price of 100 ml in each bottle.
  2. 500 ml: 1.85 ÷ 5 = $0.37. 1.5 litres = 1,500 ml: 5.10 ÷ 15 = $0.34.
  3. 750 ml: 2.70 ÷ 7.5 = $0.36.
  4. The lowest price per 100 ml is $0.34.
BottlePricePrice per 100 ml
500 ml$1.85$0.37
1.5 litres$5.10$0.34
750 ml$2.70$0.36

The lowest price per 100 ml is the best buy.

The 1.5 litre bottle

Common mistake: Multiplying when you should divide. Dollars to another currency: multiply by the rate. Another currency to dollars: divide by the rate. Check the size of your answer every time.

PractiseCalculator allowed

10 questions with instant feedback

Choose the correct answer. A calculator is allowed. Write down which way you are changing the money before you multiply or divide. Give money to the nearest cent. Questions 1–3 are warm-ups, 4–7 are at exam standard and 8–10 are challenge questions. After you answer, the feedback shows the full solution.

Score: 0 / 10Answered: 0 / 10

Warm-up (The basic skill: one or two steps.)

1.Use the rate 1 dollar = 0.85 euros. Change $460 into euros.

Not quite. This divides by the rate. To change dollars into euros, multiply.

Solution

  1. Dollars to euros: multiply by the rate.
  2. 460 × 0.85 = 391 euros.

Answer: B. 391 euros.

Correct.

Solution

  1. Dollars to euros: multiply by the rate.
  2. 460 × 0.85 = 391 euros.

Not quite. This works out 15% of 460.

Solution

  1. Dollars to euros: multiply by the rate.
  2. 460 × 0.85 = 391 euros.

Answer: B. 391 euros.

Not quite. This adds the rate. Multiply by it.

Solution

  1. Dollars to euros: multiply by the rate.
  2. 460 × 0.85 = 391 euros.

Answer: B. 391 euros.

2.Use the rate 1 dollar = 110 yen. Change 19,250 yen into dollars.

Not quite. This multiplies by the rate. To change yen into dollars, divide.

Solution

  1. Yen to dollars: divide by the rate.
  2. 19,250 ÷ 110 = $175.

Answer: C. $175.

Not quite. This divides by 100, not by 110.

Solution

  1. Yen to dollars: divide by the rate.
  2. 19,250 ÷ 110 = $175.

Answer: C. $175.

Correct.

Solution

  1. Yen to dollars: divide by the rate.
  2. 19,250 ÷ 110 = $175.

Not quite. This subtracts the rate. Divide by it.

Solution

  1. Yen to dollars: divide by the rate.
  2. 19,250 ÷ 110 = $175.

Answer: C. $175.

3.Eggs are sold in packs of 10 for $3.70, 6 for $2.34, 12 for $4.56 and 30 for $11.25. Which pack is the best buy?

Not quite. This is the cheapest pack, not the cheapest egg: 2.34 ÷ 6 = 39 cents each.

Solution

  1. Find the price of one egg in each pack.
  2. 10: 37 cents. 6: 39 cents. 12: 38 cents. 30: 37.5 cents.
  3. The pack of 10 has the lowest price per egg.

Answer: D. The pack of 10.

Not quite. 4.56 ÷ 12 = 38 cents each, which is more than 37 cents.

Solution

  1. Find the price of one egg in each pack.
  2. 10: 37 cents. 6: 39 cents. 12: 38 cents. 30: 37.5 cents.
  3. The pack of 10 has the lowest price per egg.

Answer: D. The pack of 10.

Not quite. The biggest pack is not always the best buy: 11.25 ÷ 30 = 37.5 cents each.

Solution

  1. Find the price of one egg in each pack.
  2. 10: 37 cents. 6: 39 cents. 12: 38 cents. 30: 37.5 cents.
  3. The pack of 10 has the lowest price per egg.

Answer: D. The pack of 10.

Correct.

Solution

  1. Find the price of one egg in each pack.
  2. 10: 37 cents. 6: 39 cents. 12: 38 cents. 30: 37.5 cents.
  3. The pack of 10 has the lowest price per egg.

Exam standard (Several steps, like real exam questions.)

4.Use the exchange rates in the table. Kai changes 600 euros into pounds. How many pounds does he get?

CurrencyAmount for $1
euros0.9
pounds0.75
yen150

Use these rates. (They are for practice, not today’s real rates.)

Correct.

Solution

  1. Euros to dollars: 600 ÷ 0.9 = $666.666….
  2. Dollars to pounds: 666.666… × 0.75.
  3. = 500 pounds.

Not quite. This multiplies by 0.9. To change euros into dollars, divide by 0.9.

Solution

  1. Euros to dollars: 600 ÷ 0.9 = $666.666….
  2. Dollars to pounds: 666.666… × 0.75.
  3. = 500 pounds.

Answer: A. 500 pounds.

Not quite. This uses the two rates the wrong way round.

Solution

  1. Euros to dollars: 600 ÷ 0.9 = $666.666….
  2. Dollars to pounds: 666.666… × 0.75.
  3. = 500 pounds.

Answer: A. 500 pounds.

Not quite. This treats the euros as dollars. Change the euros into dollars first.

Solution

  1. Euros to dollars: 600 ÷ 0.9 = $666.666….
  2. Dollars to pounds: 666.666… × 0.75.
  3. = 500 pounds.

Answer: A. 500 pounds.

5.Rui changes $850 into euros at the rate 1 dollar = 0.88 euros. The booth keeps 3% of the euros as commission. How many euros does Rui get?

Not quite. This forgets the commission.

Solution

  1. 850 × 0.88 = 748 euros.
  2. Commission: 3% of 748 = 22.44 euros.
  3. Rui gets 748 − 22.44 = 725.56 euros.

Answer: B. 725.56 euros.

Correct.

Solution

  1. 850 × 0.88 = 748 euros.
  2. Commission: 3% of 748 = 22.44 euros.
  3. Rui gets 748 − 22.44 = 725.56 euros.

Not quite. This adds the commission. Commission is taken off.

Solution

  1. 850 × 0.88 = 748 euros.
  2. Commission: 3% of 748 = 22.44 euros.
  3. Rui gets 748 − 22.44 = 725.56 euros.

Answer: B. 725.56 euros.

Not quite. This is the commission. The question asks how many euros Rui gets.

Solution

  1. 850 × 0.88 = 748 euros.
  2. Commission: 3% of 748 = 22.44 euros.
  3. Rui gets 748 − 22.44 = 725.56 euros.

Answer: B. 725.56 euros.

6.Mel wants exactly 1,764 euros. Use the rate 1 dollar = 0.9 euros. The booth first takes 2% of the dollars she hands over as commission. How many dollars must she hand over?

Not quite. This forgets the commission. Only 98% of her dollars are changed.

Solution

  1. Dollars to be changed: 1,764 ÷ 0.9 = $1,960.
  2. This is 98% of what she hands over.
  3. 1,960 ÷ 0.98 = $2,000.

Answer: C. $2,000.

Not quite. This adds 2% of $1,960. The $1,960 is 98% of what she hands over, so divide by 0.98.

Solution

  1. Dollars to be changed: 1,764 ÷ 0.9 = $1,960.
  2. This is 98% of what she hands over.
  3. 1,960 ÷ 0.98 = $2,000.

Answer: C. $2,000.

Correct.

Solution

  1. Dollars to be changed: 1,764 ÷ 0.9 = $1,960.
  2. This is 98% of what she hands over.
  3. 1,960 ÷ 0.98 = $2,000.

Not quite. This multiplies by the rate. To find dollars from euros, divide.

Solution

  1. Dollars to be changed: 1,764 ÷ 0.9 = $1,960.
  2. This is 98% of what she hands over.
  3. 1,960 ÷ 0.98 = $2,000.

Answer: C. $2,000.

7.Use the rate 1 dollar = 0.8 euros. Which working shows that 520 euros is worth $650?

Not quite. This changes the money the wrong way. Euros to dollars means divide.

Solution

  1. Euros to dollars: divide by the rate.
  2. 520 ÷ 0.8 = 650.
  3. So 520 euros is worth $650 ✓.

Answer: B. 520 ÷ 0.8 = 650.

Correct.

Solution

  1. Euros to dollars: divide by the rate.
  2. 520 ÷ 0.8 = 650.
  3. So 520 euros is worth $650 ✓.

Not quite. This adds 20%. Dividing by 0.8 is the same as adding 25%.

Solution

  1. Euros to dollars: divide by the rate.
  2. 520 ÷ 0.8 = 650.
  3. So 520 euros is worth $650 ✓.

Answer: B. 520 ÷ 0.8 = 650.

Not quite. The rate is 0.8, not 8.

Solution

  1. Euros to dollars: divide by the rate.
  2. 520 ÷ 0.8 = 650.
  3. So 520 euros is worth $650 ✓.

Answer: B. 520 ÷ 0.8 = 650.

Challenge (Harder problems that mix ideas or need reasoning.)

8.Ola changes $2,000 into euros at 1 dollar = 0.92 euros. She spends 1,150 euros. She changes the rest back into dollars at 1 dollar = 0.95 euros. How many dollars does she get back, to the nearest cent?

Not quite. This multiplies by the rate. Euros to dollars means divide.

Solution

  1. Euros: 2,000 × 0.92 = 1,840 euros.
  2. Left: 1,840 − 1,150 = 690 euros.
  3. Back to dollars: 690 ÷ 0.95 = 726.315…, which is $726.32.

Answer: D. $726.32.

Not quite. This uses the first rate. The rate for changing back is 0.95.

Solution

  1. Euros: 2,000 × 0.92 = 1,840 euros.
  2. Left: 1,840 − 1,150 = 690 euros.
  3. Back to dollars: 690 ÷ 0.95 = 726.315…, which is $726.32.

Answer: D. $726.32.

Not quite. This changes back the euros she spent. Change back what is left.

Solution

  1. Euros: 2,000 × 0.92 = 1,840 euros.
  2. Left: 1,840 − 1,150 = 690 euros.
  3. Back to dollars: 690 ÷ 0.95 = 726.315…, which is $726.32.

Answer: D. $726.32.

Correct.

Solution

  1. Euros: 2,000 × 0.92 = 1,840 euros.
  2. Left: 1,840 − 1,150 = 690 euros.
  3. Back to dollars: 690 ÷ 0.95 = 726.315…, which is $726.32.

9.Rice is sold in three shops. Shop P: a 1.5 kg bag for $4.20. Shop Q: 2 kg bags at $6 each, with the second bag half price. Shop R: 500 g bags at $1.50 each, 3 for the price of 2. Which shop is cheapest per kilogram, and what is its price per kilogram?

Correct.

Solution

  1. P: 4.20 ÷ 1.5 = $2.80 per kg.
  2. Q: two bags (4 kg) cost 6 + 3 = $9, so 9 ÷ 4 = $2.25 per kg.
  3. R: three bags (1.5 kg) cost 2 × 1.50 = $3, so 3 ÷ 1.5 = $2 per kg.

Not quite. This misses the offer at shop R. With it, 1.5 kg costs $3, which is $2 per kg.

Solution

  1. P: 4.20 ÷ 1.5 = $2.80 per kg.
  2. Q: two bags (4 kg) cost 6 + 3 = $9, so 9 ÷ 4 = $2.25 per kg.
  3. R: three bags (1.5 kg) cost 2 × 1.50 = $3, so 3 ÷ 1.5 = $2 per kg.

Answer: A. Shop R: $2 per kg.

Not quite. This misses both offers. With them, shops Q and R are cheaper.

Solution

  1. P: 4.20 ÷ 1.5 = $2.80 per kg.
  2. Q: two bags (4 kg) cost 6 + 3 = $9, so 9 ÷ 4 = $2.25 per kg.
  3. R: three bags (1.5 kg) cost 2 × 1.50 = $3, so 3 ÷ 1.5 = $2 per kg.

Answer: A. Shop R: $2 per kg.

Not quite. This is shop R without its offer. With 3 for 2, it is $2 per kg.

Solution

  1. P: 4.20 ÷ 1.5 = $2.80 per kg.
  2. Q: two bags (4 kg) cost 6 + 3 = $9, so 9 ÷ 4 = $2.25 per kg.
  3. R: three bags (1.5 kg) cost 2 × 1.50 = $3, so 3 ÷ 1.5 = $2 per kg.

Answer: A. Shop R: $2 per kg.

10.Pia changes $750 into pounds. The booth keeps 2% of the pounds as commission, and Pia receives 588 pounds. What exchange rate did the booth use?

Not quite. This ignores the commission. The 588 pounds is only 98% of the pounds before commission.

Solution

  1. Before commission: 588 ÷ 0.98 = 600 pounds.
  2. Rate: 600 ÷ 750 = 0.8.
  3. So 1 dollar = 0.8 pounds.

Answer: C. 1 dollar = 0.8 pounds.

Not quite. This works out 750 ÷ 600, which is dollars per pound. The rate is pounds per dollar.

Solution

  1. Before commission: 588 ÷ 0.98 = 600 pounds.
  2. Rate: 600 ÷ 750 = 0.8.
  3. So 1 dollar = 0.8 pounds.

Answer: C. 1 dollar = 0.8 pounds.

Correct.

Solution

  1. Before commission: 588 ÷ 0.98 = 600 pounds.
  2. Rate: 600 ÷ 750 = 0.8.
  3. So 1 dollar = 0.8 pounds.

Not quite. This works out 750 ÷ 588. It ignores the commission and turns the rate upside down.

Solution

  1. Before commission: 588 ÷ 0.98 = 600 pounds.
  2. Rate: 600 ÷ 750 = 0.8.
  3. So 1 dollar = 0.8 pounds.

Answer: C. 1 dollar = 0.8 pounds.

Apply

Holiday money

Ade is going on a trip. Use the rate 1 dollar = 0.86 euros. The exchange booth takes 1.5% commission from the dollars before changing them.

1. How many euros does Ade get for $900?

2. He has 120 euros left at the end. He changes it back at 1 dollar = 0.9 euros, with no commission. How many dollars does he get, to the nearest cent?

3. On the trip, sunscreen costs 7.20 euros for 200 ml or 10.50 euros for 300 ml. Which is the better buy?

  1. Dollars changed: 900 × 0.985 = $886.50. Euros: 886.50 × 0.86 = 762.39 euros.
  2. Euros to dollars: divide. 120 ÷ 0.9 = 133.333…, so $133.33.
  3. Price per 100 ml: 7.20 ÷ 2 = 3.60 euros and 10.50 ÷ 3 = 3.50 euros. The 300 ml bottle is the better buy.

Next: the Lesson 5 exit quiz, then the unit test. The unit test has 18 multiple-choice questions and five structured problems, 44 marks in all. A calculator is allowed in both sections. Allow 70 minutes.

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