System of linear equations word problem using ratios

by aparna
(chennai)

A man bought 66 kg of 3 types of fruits namely bananas, oranges and apples. The ratio of bananas to oranges is 4:5 and that of oranges to apples is 2:3 Find out how many kg of apples were bought.

Solution

Let x be number of bananas
Let y be number of oranges
let z be number of apples

x + y + z = 66

x/y = 4/5
After cross-multiplication, 5x = 4y.
Thus, x = 4y/5

y/z = 2/3
After cross-multiplication, 2z = 3y.
Thus, z = 3y/2

Replace x and z into x + y + z = 66

4y/5 + y + 3y/2 = 66

8y/10 + 10y/10 + 15y/10 = 66

(8y + 10y + 15y)/10 = 66

33y/10 = 66

33y = 660, so y = 20

There are 20 kg of oranges

Since z = 3y/2, z = (3 × 20)/2 = 60/2 = 30

There are 30 kg of apples