Question

Perry and Katy are both saving money from their summer jobs to buy a car. If Perry had $\$150$ less, she would have exactly $\frac{1}{3}$ as much as Katy. And if Katy had twice as much, she would have exactly $3$ times as much as Perry. How much money have they saved together?

• A. $300
• B. $400
• C. $450
• D. $625
• E. $750

Answer 1

The correct option is E $750Letperrysaved$x$andKatysaved$y$

Then if perry had $150$ less than Katy is $3$ times more than Perry

$\Rightarrow y=3(x-150)$

$\Rightarrow y=3x-450$...eq1

If katy has twice as much she would have $3$ times more than Perry.

$\Rightarrow 2y=3x$

Substitute the value of $y$ from (1)

$\Rightarrow 2(3x-450)=3x$

$\Rightarrow 6x-900=3x$

$\Rightarrow 6x-3x=900$

$\Rightarrow 3x=900$

$\Rightarrow x=$300$

Substitute the value of $x=300$ in (1), we get

$\Rightarrow y=3\times 300-450$

$\Rightarrow y=900-450$

$\Rightarrow y=$450$

$\therefore$ they saved together $=$ $300+450=$750$