Question

Alice's stamp collection was 75% of the size of Raymond's. After Alice sold 40% of her stamps and Raymond sold 20% of his stamps, Alice had 140 fewer stamps than Raymond. How many stamps did Alice sell?

Answer 1

Alice sold `120` stamps

Explanation:

Alice had fewer stamps than Raymond.
Let the number of Alice's stamps be `x`.

If she had `x` stamps, then Raymond had `4/3x`

They each sold stamps:

`100%-40% = 60% and 100% -20% =80%`

Write an equation:

`60%xx x +140 = 80%xx 4/3x`

`(60x)/100 +140 = (4xx80x)/(3xx100)`

Multiply by `300` to cancel the denominators:

`(60x)/100 +140 = (4xx80x)/(3xx100)`

`(cancel300^3 xx60x)/cancel100 +42,000 = (cancel300xx4xx80x)/(cancel3xxcancel100)`

`180x +42000 = 320x`

`42000 = 140x" "larr div 140`

`300 = x`

Alice started with `300` stamps.

She sold `40/100 xx 300 = 120` stamps.

Lets's check the numbers:

Alice had `300` stamps and Raymond had `300 xx 4/3 = 400` stamps.

`300-120 = 180` stamps (Alice's)
`400 - 80 = 320` stamps (Raymond's)

`320-180 = 140`