Question

Fred and George had some savings in the ratio 3 : 4 respectively.

They decided to buy a birthday present for their little sister sharing the cost at ratio 2 : 3 respectively.

After they have bought the present, Fred has already spent half of his money. George only has £21 left over.

Find the price of the present.

Answer 1

The price of the present is £45.

Explanation:

step 1 :

Let,

Savings of Fred = 3x

Savings of George = 4x

step 2 :

share of Fred = 2y

share of George = 3y

∴ Total cost of the gift = 2y + 3y = 5y

step 3 :

According to the question given,

Fred has already spent half of his money = 3x - 2y = (1/2)3x

George only has £21 left over = 4x - 3y = 21

step 4 :

solve for x in the first equation,

3x - (3/2)x = 2y

6x - 3x = 4y

3x = 4y

x = (4/3)y

step 5 :

substitute x=(4/3)y in the second equation to find y,

4x - 3y = 21

4(4/3)y - 3y = 21

(16/3)y - 3y = 21

16y - 9y = 63

7y = 63

y = 9

step 6 :

The total cost of the gift = 2y + 3y

Price of the present = 5y = 5
`*`9 = 45