Question

The costs of 1 kg apples and 1 kg grapes are in the ratio of 9:7. The cost of 1 kg apples is Rs 20 more than the cost of 1kg grapes. Find the cost of 1 kg apples and 1 kg of grapes.

Answer 1

Apple = Rs90

Grape = Rs70

Explanation:

Given

Represent Apples with A and Grapes with G

Such that:

The ratio is

`A : G =9:7`

And the price is

`A = 20 + G`

Required

Determine the cost of 1 kg of each fruit

`A : G =9:7`

Convert to fraction

`(A)/(G) = (9)/(7)`

Cross Multiply

`7A = 9G`

Make A the subject

`A = (9)/(7)G`

Substitute
`(9)/(7)G` for A in
`A = 20 + G`

`(9)/(7)G = 20 + G`

Collect Like Terms

`(9)/(7)G - G = 20`

Take LCM

`(9G - 7G)/(7)= 20`

`(2G)/(7)= 20`

Multiply through by 7

`7 * (2G)/(7)= 20 * 7`

`2G= 20 * 7`

Divide through by 2

`(2G)/(2) = (20 * 7)/(2)`

`G = (20 * 7)/(2)`

`G = 10 * 7`

`G = 70`

Substitute 70 for G in
`A = (9)/(7)G`

`A = (9)/(7) * 70`

`A = 9 * 10`

`A = 90`