5.8 Solving Ratio Problems

Unit 5: Ratios

In this movie poster, Ryan Reynolds is 8cm. Sandra Bullock is 6cm. If Ryan Reynolds is 1.8m tall in real life, how tall is Sandra Bullock?

The ratio Ryan’s height to Sandra’s height, is 8:6.

Let h represent Sandra’s actual height, in cm.

Then, the ratio of the actual height of Ryan to the actual height of Sandra is 1.8 : h

1.8m = 180cm, so the ratio is 180:h The two ratios are equivalent. Then…

180:h = 8:6

To find the value of h, write a ratio equivalent to 8:6, with the first term 180.

Since 8 does not divide into 180 exactly, simply the ratio 8:6 first.

8:6 = 4:3 Write a ratio equivalent to 4:3 with the

first term 180. 4:3 = 180:135 (multiply both sides by 45)

So, 180:h = 180:135. So, h = 135. Sandra Bullocks actual height is 135cm or

1.35m.

Key Math Learnings: Equal Ratios can be written as a

proportion. A proportion can be solved to find the

value of an unknown term.

Find the value of each variable:a) 5:x = 40:56

b) 49:35 = 14:n