Grade 7 Proportions: Complex Proportions

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   In a jar, the ratio of red marbles to blue marbles is 5:2. There are 24 more red marbles than blue marbles. How many blue marbles are there?

   1. Red has 5 parts and blue has 2, so red has 5 − 2 = 3 more parts.
   2. Those 3 parts are the 24 extra marbles, so one part is 24 ÷ 3 = 8.
   3. Blue is 2 parts: 2 × 8 = 16.
   4. So there are 16 blue marbles.

   Answer: 16

2. Example 2

   Solve the proportion 12/9 = x/12. What is x?

   1. 12 is not a whole-number multiple of 9, so you can't just scale 12/9 up — cross-multiply instead.
   2. Cross-multiply: 9 × x = 12 × 12 = 144.
   3. Divide by 9: x = 144 ÷ 9 = 16.
   4. Check: 12 × 12 = 144 and 9 × 16 = 144 — the cross products match.
   5. So x = 16.

   Answer: 16

3. Example 3

   Solve the proportion 42/x = 35/30. What is x?

   1. x is in a denominator, so cross-multiply to bring it up into an equation.
   2. Cross-multiply: 35 × x = 42 × 30 = 1260.
   3. Divide by 35: x = 1260 ÷ 35 = 36.
   4. Check: 42 × 30 = 1260 and 36 × 35 = 1260 — the cross products match.
   5. So x = 36.

   Answer: 36