Worksheet: Solving Proportions with 3 Ratios

In this worksheet, we will practice finding unknown information when two or three proportions are compared.

Q1:

Given that 2 1 𝑎 = 7 9 = 𝑏 3 6 , find the values of 𝑎 and 𝑏 .

  • A 𝑎 = 2 1 and 𝑏 = 2 8
  • B 𝑎 = 2 7 and 𝑏 = 3 6
  • C 𝑎 = 9 and 𝑏 = 7
  • D 𝑎 = 2 7 and 𝑏 = 2 8

Q2:

Fill in the blanks: 5 2 = 1 5 = 3 = 1 4 = 8 4 5 .

  • A37.5, 7.5, 35, 20
  • B37.5, 1.2, 35, 3.2
  • C6, 1.2, 5.6, 3.2
  • D6, 1.2, 37, 20

Q3:

If 0 . 8 0 . 4 = 7 . 8 = 9 . 5 = 4 . 3 = 3 . 5 , use the method of cross multiplication to find the missing numbers.

  • A 1 5 . 6 , 1 9 , 8 . 6 , 7
  • B 3 . 9 , 4 . 7 5 , 8 . 6 , 1 . 7 5
  • C 3 . 9 , 4 . 7 5 , 2 . 1 5 , 1 . 7 5
  • D 1 5 . 6 , 4 . 7 5 , 8 . 6 , 1 . 7 5

Q4:

If 2 𝑎 9 𝑏 = 3 2 , find 𝑎 𝑏 .

  • A 1 3
  • B 4 2 7
  • C3
  • D 2 7 4

Q5:

If 2 𝑎 = 9 𝑏 , determine 1 3 𝑏 2 𝑎 .

  • A 1 1 7 4
  • B 9 1 3
  • C 4 1 1 7
  • D 1 3 9

Q6:

Given that 𝑥 1 5 = 𝑦 5 = 𝑧 7 = 7 𝑥 6 𝑦 + 4 𝑧 𝑎 , calculate the value of 𝑎 .

Q7:

If 4 6 𝑥 = 2 9 𝑦 , determine the value of 𝑥 𝑦 .

  • A 1 334
  • B 4 6 2 9
  • C 1 1 3 3 4
  • D 2 9 4 6

Q8:

Given that the ratio 1 9 1 4 is the same as 𝑥 5 6 , determine the value of 𝑥 .

Q9:

If 𝑎 7 = 𝑏 4 = 𝑐 1 4 = 6 𝑎 7 𝑏 + 2 𝑐 3 𝑥 , find the value of 𝑥 .

Q10:

If 𝑥 1 9 = 𝑦 1 1 = 3 𝑥 𝑦 𝑎 , find the value of 𝑎 .

Q11:

Given that 𝑦 𝑧 = 𝑧 𝑛 = 𝑛 𝑚 = 4 1 1 , determine the solution set of the equation 𝑦 𝑥 2 𝑧 𝑥 + 𝑛 = 0 .

  • A 1 1 4
  • B 4 1 1
  • C 4 1 1
  • D 1 1 4

Q12:

Given that 8 . 7 𝑎 = 2 7 = 𝑏 4 0 . 6 , find the values of 𝑎 and 𝑏 .

  • A 𝑎 = 6 0 . 9 and 𝑏 = 2 8 4 . 2
  • B 𝑎 = 1 . 2 4 and 𝑏 = 5 . 8
  • C 𝑎 = 1 . 2 4 and 𝑏 = 2 8 4 . 2
  • D 𝑎 = 3 0 . 4 5 and 𝑏 = 1 1 . 6

Q13:

If 1 5 𝑎 𝑏 𝑐 = 5 𝑎 8 𝑏 2 , determine the value of 𝑐 where both 𝑐 and 𝑏 0 .

  • A 2 4 𝑎 𝑏
  • B 𝑎 𝑏 2
  • C 2 4 𝑎 𝑏 2
  • D 2 4 𝑎 𝑏 2

Q14:

If 𝑥 1 4 = 𝑦 8 = 9 𝑥 + 𝑦 𝑎 , find the value of 𝑎 .

Q15:

If 5 𝑥 = 2 𝑦 = 𝑎 𝑦 𝑥 , find the value of 𝑎 .

Q16:

If 𝑥 𝑦 = 𝑦 𝑧 = 𝑧 2 = 4 , find the value of 𝑥 .

Q17:

In the box below, corresponding numbers on each row are proportional. Find the values of 𝑎 and 𝑏 .

3 13 𝑎
15 𝑏 5
  • A 𝑎 = 1 , 𝑏 = 3 9
  • B 𝑎 = 2 5 , 𝑏 = 6 5
  • C 𝑎 = 2 5 , 𝑏 = 3 9
  • D 𝑎 = 1 , 𝑏 = 6 5

Q18:

What is the value of 𝑥 , the first proportional of the numbers 𝑥 , 6 , 15 and 3 6 ?

Q19:

If 𝑎 𝑏 = 𝑐 𝑑 = 𝑒 𝑓 , then 3 𝑎 + 1 5 𝑐 + 1 2 𝑒 3 𝑏 + + 1 2 𝑓 = 𝑎 𝑏 . Find the missing term.

  • A 1 5 𝑑
  • B 𝑑
  • C 𝑑
  • D 1 5 𝑑

Q20:

If 1 6 9 𝑥 = 1 9 6 𝑦 2 2 , where 𝑥 + and 𝑦 + , find the value of 𝑦 𝑥 .

  • A 1 6 9 1 9 6
  • B 1 4 1 3
  • C 1 9 6 1 6 9
  • D 1 3 1 4

Q21:

𝑎 + 𝑏 𝑎 = 𝑎 2 .

  • A 𝑎 + 𝑎 𝑏 2 2
  • B 𝑎 + 𝑏 2 2
  • C 2 𝑎 + 2 𝑏
  • D 𝑎 + 𝑎 𝑏 2

Q22:

Fill in the blanks: 1 0 3 = 9 0 = 2 = 1 2 = 3 0 9 1 0 .

  • A300, 6.67, 40, 100
  • B300, 0.6, 40, 9
  • C27, 0.6, 3.6, 9
  • D27, 0.6, 43, 100

Q23:

Fill in the blanks: 5 3 = 3 5 = 1 0 = 1 2 = 2 7 3 5 .

  • A58.33, 16.67, 20, 45
  • B58.33, 6, 20, 16.2
  • C21, 6, 7.2, 16.2
  • D21, 6, 21, 45

Q24:

Fill in the blanks: 8 5 = 7 2 = 6 = 1 4 = 3 0 3 8 .

  • A115.2, 9.6, 22.4, 48
  • B115.2, 3.75, 22.4, 18.75
  • C45, 3.75, 8.75, 18.75
  • D45, 3.75, 23, 48

Q25:

Fill in the blanks: 6 5 = 6 0 = 3 = 1 5 = 2 0 5 6 .

  • A72, 3.6, 18, 24
  • B72, 2.5, 18, 16.67
  • C50, 2.5, 12.5, 16.67
  • D50, 2.5, 19, 24

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