Question

Cindy and Kendra both want to buy the same dress. The dress costs 2/3 of Cindy's savings, and it costs 1/2 of Kendra's savings. If Kendra has $30 more savings tahn Cindy, how much does the dress cost?Answer: $______

Answer 1

To determine the cost of the dress:

Let the cost of the dress = C

Let the cindy's savings = x

Let the kendra savings = y

Kendra has $30 more savings than Cindy

`y=30+x\ldots..\text{. }(1)`

The dress cost = 2/3 of cindy's savings and = 1/2 of kendra's savings

`\begin{gathered} C=(2)/(3)x=(1)/(2)y \\ (2)/(3)x=(1)/(2)y \\ \text{cross multiply} \\ 4x=3y \\ 4x-3y=0\ldots\ldots(2) \end{gathered}`

substitute y in equation (2)

`\begin{gathered} 4x-3y=0 \\ 4x-3(30+x)=0 \\ 4x-90-3x=0 \\ 4x-3x=0+90 \\ x=90 \end{gathered}`

Cost of the dress = 2/3 of cindy's

`C=(2)/(3)x=(2)/(3)(90)=\text{ \$60}`

Therefore the cost of the dress = $60