Question

Sheila went shopping and spent $120 on a coat. She then used 2/3 of the remaining money to buy a dress. She was left with 1/5 of her original amount of money. How much did Sheila have at first?

Answer 1

== x - 120 + (2/3)*(x - 120) + (1/5)*(x) = x (original amount)

Answer 2

Find out the how much did Sheila have at first .

To proof

Let us assume that the original amount of money be x .

As given

Sheila went shopping and spent $120 on a coat.

Than

money sheila has = x - 120

`She\ then\ used\ (2)/(3)\ of\ the\ remaining\ money\ to\ buy\ a\ dress`

`She\ was\ left\ with\ (1)/(5)\ of\ her\ original\ amount\ of\ money.`

Than the equation becomes

`120 + (2*(x- 120))/(3) +(1x)/(5) = x`

L.C.M of (5,3) = 15

`1800+{10x -1200 +3x}=15x`

solving

600 +13x = 15x

600 = 15x - 13x

600 = 2x

`x = (600)/(2)`

x = $300

The shelia have money be $300 .

Hence proved