Question

Luke and Ella have money in their bank account in the ratio 7:8

Luke gives £2 to Ella, and the ratio becomes 4:5.

Work out the original amount of money that Ella had.

Answer 1

$48

Explanation:

Ratios can be written as fractions.

1) Initially, Luke had 7x money, Ella had 8x money. Luke gives $2 to Ella. So, Luke now has 7x - 2 money and Ella has 8x + 2. The total amount of money is 4:5. These could be shown as fractions.

7x - 2/8x + 2 = 4/5

4(8x + 2) = 5(7x - 2)

32x + 8 = 35x - 10

8 + 10 = 35x - 32x

18 = 3x

18/3 = x

x = 6

2) Substitute the result (x = 6) into 7x:8x.

= 7(6)

= 42

= 8(6)

= 48