Question

Find the difference between the largest share and the smaller share in each of the following ratios when $192 is shared among three people

A)2:5:13
B)22:5:14

Answer 1

A) For the ratio 2:5:13, we can write:

2x + 5x + 13x = 192

Simplifying, we get:

20x = 192

x = 9.6

Therefore, the amounts received by the three people are:

2x = 19.2

5x = 48

13x = 124.8

The smallest share is 19.2 and the largest share is 124.8. Hence, the difference between the largest share and the smallest share is:

124.8 - 19.2 = 105.6

Therefore, the difference between the largest share and the smallest share is 105.6.

B) For the ratio 22:5:14, we can write:

22x + 5x + 14x = 192

Simplifying, we get:

41x = 192

x = 4.68

Therefore, the amounts received by the three people are:

22x = 102.96

5x = 23.4

14x = 65.52

The smallest share is 23.4 and the largest share is 102.96. Hence, the difference between the largest share and the smallest share is:

102.96 - 23.4 = 79.56

Therefore, the difference between the largest share and the smallest share is 79.56.