Question

Sonia has five more pairs of shoes than Danielle. Imelda has twice as many pairs of shoes as Sonia. Altogether, the girls have 39 pairs of shoes. How many more pairs of shoes does Imelda have than Sonia and Danielle have combined

Answer 1

Imelda has 5 more pairs of shoes than Sonia and Danielle have combined.

Explanation:

This question can be solved by a system of equations.

I am going to say that:

Sonia has x pairs of shoes.

Danielle has y pairs of shoes.

Imelda has z pairs of shoes.

Sonia has five more pairs of shoes than Danielle.

This means that

`x = y + 5`

Imelda has twice as many pairs of shoes as Sonia.

This means that
`z = 2x`

Altogether, the girls have 39 pairs of shoes.

This means that
`x + y + z = 39`

Since
`x = y + 5, z = 2x = 2(y + 5)`

`x + y + z = 39`

`y + 5 + y + 2y + 10 = 39`

`4y + 15 = 39`

`4y = 24`

`y = (24)/(4)`

`y = 6`

Danielle has 6 pairs.

Sonia:

`x = y + 5 = 6 + 5 = 11`

Sonia has 11 pairs.

Imelda:

`z = 2x = 2(11) = 22`

Imelda has 22 pairs.

How many more pairs of shoes does Imelda have than Sonia and Danielle have combined?

Imelda has 22 pairs.

Sonia and Danielle combined have 11 + 6 = 17 pairs.

22 - 17 = 5

Imelda has 5 more pairs of shoes than Sonia and Danielle have combined.