Answer:
$37.50
Step-by-step explanation:
Let beginning amount of money be
"s" for Sorin
and
"j" for Joel
The ratio is 4:7, so we can write:
[tex]\frac{s}{j}=\frac{4}{7}[/tex]
Also,
After sorin GOT 50 MORE, the ratio became 8:7, so we can write:
[tex]\frac{s+50}{j}=\frac{8}{7}[/tex]
Let's cross multiply 1st equation and find an expression for "j":
[tex]\frac{s}{j}=\frac{4}{7}\\7s=4j\\j=\frac{7s}{4}[/tex]
Now, we put this into 2nd and solve for s:
[tex]\frac{s+50}{j}=\frac{8}{7}\\\frac{s+50}{\frac{7s}{4}}=\frac{8}{7}[/tex]
Cross multiply and solve for s:
[tex]\frac{s+50}{\frac{7s}{4}}=\frac{8}{7}\\7(s+50)=8*\frac{7s}{4}\\7s+350=14s\\7s=350\\s=50[/tex]
So, "j" would be:
[tex]j=\frac{7s}{4}\\j=\frac{7(50)}{4}\\j=87.5[/tex]
Sorin's allowance is $50
Joel's allowance is $87.50
Joel had 87.50 - 50 = $37.50 more than Sorin
