Question

The ratio of Sorin's weekly allowance to Joel's weekly allowance was 4:7. After Sorin received $50 frim his parents, the ratio became 8:7. How much more money did Joel have than Sorin in the beginning?

Answer 1

$37.50

Explanation:

Let beginning amount of money be

"s" for Sorin

and

"j" for Joel

The ratio is 4:7, so we can write:

`(s)/(j)=(4)/(7)`

Also,

After sorin GOT 50 MORE, the ratio became 8:7, so we can write:

`(s+50)/(j)=(8)/(7)`

Let's cross multiply 1st equation and find an expression for "j":

`(s)/(j)=(4)/(7)\\7s=4j\\j=(7s)/(4)`

Now, we put this into 2nd and solve for s:

`(s+50)/(j)=(8)/(7)\\(s+50)/((7s)/(4))=(8)/(7)`

Cross multiply and solve for s:

`(s+50)/((7s)/(4))=(8)/(7)\\7(s+50)=8*(7s)/(4)\\7s+350=14s\\7s=350\\s=50`

So, "j" would be:

`j=(7s)/(4)\\j=(7(50))/(4)\\j=87.5`

Sorin's allowance is $50

Joel's allowance is $87.50

Joel had 87.50 - 50 = $37.50 more than Sorin