Ratios & Ratio Tables — Challenge

A ratio compares two amounts, and scaling both by the same factor leaves it unchanged.

What these problems cover

These questions use 1 idea from the course. Follow any of them for a definition, where it is taught, and what it leads to.

Problem 1

In a mixture of peanuts and cashews the ratio by weight of peanuts to cashews is 5 to 3. A bag holds 40 pounds of the mixture. How many pounds of cashews does it hold?

  1. 12
  2. 15
  3. 18
  4. 24
  5. 25
Worked answer

15

A ratio of 5 to 3 divides the mixture into 5+3 = 8 equal parts.

Each part weighs 408 = 5 pounds.

Cashews take 3 parts, so they weigh 3· 5 = 15 pounds, and the peanuts weigh the other 25.

Problem 2

The ratio of boys to girls in a choir is 3 to 4. There are 28 girls. How many boys are there?

  1. 18
  2. 21
  3. 24
  4. 32
  5. 35
Worked answer

21

The girls' share is 4 parts and equals 28, so one part is 284 = 7 singers.

The boys' share is 3 parts, so there are 3· 7 = 21 boys.

Problem 3

Which ratio is equivalent to 8:20?

  1. 2:5
  2. 4:5
  3. 1:3
  4. 5:2
  5. 8:5
Worked answer

2:5

Divide both parts by their greatest common factor. The greatest common factor of 8 and 20 is 4.

8÷ 4 = 2 and 20÷ 4 = 5, so 8:20 = 2:5. The order matters, so 5:2 is a different ratio.

Problem 4

A jar holds red and blue marbles in the ratio 3 to 7. There are 30 marbles in all. How many are red?

  1. 9
  2. 10
  3. 12
  4. 14
  5. 21
Worked answer

9

The ratio gives 3+7 = 10 parts in total, so each part is 3010 = 3 marbles.

Red takes 3 parts: 3· 3 = 9 red marbles, leaving 21 blue.

Problem 5

A recipe uses sugar and flour in the ratio 2 to 3. A baker uses 12 cups of flour. How many cups of sugar are needed?

  1. 6
  2. 8
  3. 9
  4. 18
  5. 24
Worked answer

8

Flour is 3 parts and equals 12 cups, so one part is 4 cups.

Sugar is 2 parts: 2· 4 = 8 cups.

Problem 6

Write the ratio 18:24 in its lowest terms.

  1. 3:4
  2. 4:3
  3. 2:3
  4. 9:12
  5. 6:8
Worked answer

3:4

The greatest common factor of 18 and 24 is 6.

18÷ 6 = 3 and 24÷ 6 = 4, giving 3:4.

9:12 and 6:8 are equal to the same ratio but are not in lowest terms.

Problem 7

In a class the ratio of left-handed to right-handed pupils is 1 to 8. There are 36 pupils. How many are left-handed?

  1. 4
  2. 5
  3. 6
  4. 8
  5. 9
Worked answer

4

The ratio gives 1+8 = 9 parts, so one part is 369 = 4 pupils.

Left-handed pupils are 1 part, so there are 4 of them.

Problem 8

Two numbers are in the ratio 5 to 7 and they differ by 6. What is the smaller number?

  1. 10
  2. 15
  3. 21
  4. 25
  5. 30
Worked answer

15

Write the numbers as 5k and 7k so that their ratio is 5 to 7 whatever k is.

Their difference is 7k-5k = 2k, and that equals 6, so k = 3.

The smaller number is 5k = 15, and the larger is 21. They differ by 6 as required.

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