Percents — Challenge

Per cent means per hundred, so every percent is a fraction with a hundred underneath.

What these problems cover

These questions use 2 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.

Problem 1

A school library holds 250 books. Exactly 18% of them are picture books. How many picture books does the library hold?

  1. 36
  2. 40
  3. 45
  4. 48
  5. 50
Worked answer

45

A percent is a number of hundredths, so 18% of 250 means 18100· 250.

18100· 250 = 18·250100 = 18· 2.5 = 45 picture books.

Problem 2

A jacket is priced at $64. During a sale its price is reduced by 25%. What is the sale price in dollars?

  1. 16
  2. 39
  3. 44
  4. 48
  5. 52
Worked answer

48

Taking 25% off leaves 100% - 25% = 75% of the price, so multiply by 0.75 rather than subtracting twice.

0.75· 64 = 48 dollars. As a check, 25% of 64 is 16, and 64-16=48.

Problem 3

A bus has 28 seats and 7 of them are taken. What percent of the seats are taken?

  1. 20%
  2. 25%
  3. 28%
  4. 32%
  5. 40%
Worked answer

25%

The fraction taken is 728 = 14.

A percent is hundredths, so write the fraction with denominator 100: 14 = 25100 = 25%.

Problem 4

The price of a bicycle tyre rose from $20 to $23. By what percent did the price increase?

  1. 3%
  2. 10%
  3. 13%
  4. 14%
  5. 15%
Worked answer

15%

Percent increase compares the change with the original price, not with the new one.

The change is 23-20=3 dollars, so the increase is 320 = 15100 = 15%.

Problem 5

In a class of 35 pupils, 60% walk to school. How many pupils walk to school?

  1. 21
  2. 24
  3. 25
  4. 28
  5. 30
Worked answer

21

60% = 60100 = 35, and fifths are easy to take of 35.

35· 35 = 3· 7 = 21 pupils.

Problem 6

A phone plan costs $45 a month at full price. A new customer pays 20% less for the first six months and the full price for the next six months. How many dollars do they pay in the first year?

  1. $432
  2. $459
  3. $486
  4. $513
  5. $540
Worked answer

$486

Six discounted months cost 6· 0.80· 45 = 6· 36 = 216 dollars.

Six full months cost 6· 45 = 270 dollars.

The year costs 216+270 = 486 dollars. Note it is not 20% off the whole year, which would be 432.

Problem 7

15% of a number is 9. What is the number?

  1. 45
  2. 54
  3. 58
  4. 60
  5. 72
Worked answer

60

Write the sentence as an equation: 0.15· n = 9.

Divide both sides by 0.15: n = 90.15 = 90015 = 60.

Check: 15% of 60 is 9.

Problem 8

A shop takes 30% off every price, then takes a further 10% off at the till. A single discount of what percent would give the same final price?

  1. 36%
  2. 37%
  3. 38%
  4. 40%
  5. 60%
Worked answer

37%

Discounts multiply rather than add. After both, a customer pays 0.70· 0.90 = 0.63 of the original price.

Paying 63% means a discount of 100% - 63% = 37%, which is less than the 40% that adding the two discounts would suggest.

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