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Lesson: Solving Proportions with 3 Ratios

Video

13:15

Sample Question Videos

Worksheet • 25 Questions • 2 Videos

Q1:

Given that 2 1 π‘Ž = 7 9 = 𝑏 3 6 , find the values of π‘Ž and 𝑏 .

  • A π‘Ž = 2 7 and 𝑏 = 2 8
  • B π‘Ž = 2 7 and 𝑏 = 3 6
  • C π‘Ž = 9 and 𝑏 = 7
  • D π‘Ž = 2 1 and 𝑏 = 2 8

Q2:

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

  • A6, 1.2, 37, 20
  • B37.5, 1.2, 35, 3.2
  • C6, 1.2, 5.6, 3.2
  • D37.5, 7.5, 35, 20

Q3:

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

  • A 1 5 . 6 , 4 . 7 5 , 8 . 6 , 1 . 7 5
  • 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 , 1 9 , 8 . 6 , 7

Q4:

If 2 π‘Ž 9 𝑏 = 3 2 , find π‘Ž 𝑏 .

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

Q5:

If 2 π‘Ž = 9 𝑏 , determine 1 3 𝑏 2 π‘Ž .

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

Q6:

Given that π‘₯ 1 5 = 𝑦 5 = 𝑧 7 = 7 π‘₯ βˆ’ 6 𝑦 + 4 𝑧 π‘Ž , calculate the value of π‘Ž .

Q7:

If 4 6 π‘₯ = 2 9 𝑦 , determine the value of π‘₯ 𝑦 .

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

Q8:

Given that the ratio 1 9 ∢ 1 4 is the same as π‘₯ ∢ 5 6 , determine the value of π‘₯ .

Q9:

If π‘Ž 7 = 𝑏 4 = 𝑐 1 4 = 6 π‘Ž βˆ’ 7 𝑏 + 2 𝑐 3 π‘₯ , find the value of π‘₯ .

Q10:

If π‘₯ 1 9 = 𝑦 1 1 = 3 π‘₯ βˆ’ 𝑦 π‘Ž , find the value of π‘Ž .

Q11:

Given that 𝑦 𝑧 = 𝑧 𝑛 = 𝑛 π‘š = 4 1 1 , determine the solution set of the equation 𝑦 π‘₯ βˆ’ 2 𝑧 π‘₯ + 𝑛 = 0  .

  • A  1 1 4 
  • B  4 1 1 
  • C  βˆ’ 4 1 1 
  • D  βˆ’ 1 1 4 

Q12:

Given that 8 . 7 π‘Ž = 2 7 = 𝑏 4 0 . 6 , find the values of π‘Ž and 𝑏 .

  • A π‘Ž = 3 0 . 4 5 and 𝑏 = 1 1 . 6
  • B π‘Ž = 1 . 2 4 and 𝑏 = 5 . 8
  • C π‘Ž = 1 . 2 4 and 𝑏 = 2 8 4 . 2
  • D π‘Ž = 6 0 . 9 and 𝑏 = 2 8 4 . 2

Q13:

If 1 5 π‘Ž 𝑏 𝑐 = 5 π‘Ž 8 𝑏 2 , determine the value of 𝑐 where both 𝑐 and 𝑏 β‰  0 .

  • A 2 4 π‘Ž 𝑏 2
  • B π‘Ž 𝑏 2
  • C 2 4 π‘Ž 𝑏 2
  • D 2 4 π‘Ž 𝑏

Q14:

If π‘₯ 1 4 = 𝑦 8 = 9 π‘₯ + 𝑦 π‘Ž , find the value of π‘Ž .

Q15:

If 5 π‘₯ = 2 𝑦 = π‘Ž 𝑦 βˆ’ π‘₯ , find the value of π‘Ž .

Q16:

If π‘₯ 𝑦 = 𝑦 𝑧 = 𝑧 2 = 4 , find the value of π‘₯ .

Q17:

In the box below, corresponding numbers on each row are proportional. Find the values of π‘Ž and 𝑏 .

3 13 π‘Ž
15 𝑏 5
  • A π‘Ž = 1 , 𝑏 = 6 5
  • B π‘Ž = 2 5 , 𝑏 = 6 5
  • C π‘Ž = 2 5 , 𝑏 = 3 9
  • D π‘Ž = 1 , 𝑏 = 3 9

Q18:

What is the value of π‘₯ , the first proportional of the numbers π‘₯ , √ 6 , 15 and 3 √ 6 ?

Q19:

If π‘Ž 𝑏 = 𝑐 𝑑 = 𝑒 𝑓 , then 3 π‘Ž + 1 5 𝑐 + 1 2 𝑒 3 𝑏 + β‹― + 1 2 𝑓 = π‘Ž 𝑏 . Find the missing term.

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

Q20:

If 1 6 9 π‘₯ = 1 9 6 𝑦 2 2 , where π‘₯ ∈ ℝ + and 𝑦 ∈ ℝ + , find the value of 𝑦 π‘₯ .

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

Q21:

π‘Ž + 𝑏 π‘Ž = β‹― π‘Ž 2 .

  • A π‘Ž + π‘Ž 𝑏 2
  • B π‘Ž + 𝑏 2 2
  • C 2 π‘Ž + 2 𝑏
  • D π‘Ž + π‘Ž 𝑏 2 2

Q22:

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

  • A27, 0.6, 43, 100
  • B300, 0.6, 40, 9
  • C27, 0.6, 3.6, 9
  • D300, 6.67, 40, 100

Q23:

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

  • A21, 6, 21, 45
  • B58.33, 6, 20, 16.2
  • C21, 6, 7.2, 16.2
  • D58.33, 16.67, 20, 45

Q24:

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

  • A45, 3.75, 23, 48
  • B115.2, 3.75, 22.4, 18.75
  • C45, 3.75, 8.75, 18.75
  • D115.2, 9.6, 22.4, 48

Q25:

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

  • A50, 2.5, 19, 24
  • B72, 2.5, 18, 16.67
  • C50, 2.5, 12.5, 16.67
  • D72, 3.6, 18, 24
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