Question

Sally has five times as much money as Fred. If Fred earns $50 and Sally spends $125, Sally will then have twice as much money as Fred. How much money do Sally and Fred have before and after spending $125 and earning $50, respectively?

Answer 1

see the explanation

Explanation:

Let

x ----> the amount of money that Sally has in dollars

y ---> the amount of money that Fred has in dollars

we know that

`x=5y` ----> equation A

`x-125=2(y+50)` ----> equation B

Solve the system of equations by substitution

Substitute equation A in equation B

`5y-125=2(y+50)`

Solve for y

`5y-125=2y+100`

`5y-2y=100+125`

`3y=225`

`y=75`

Find the value of x

`x=5(75)=375`

therefore

Before Sally and Fred spending $125 and earning $50, respectively

Sally has $375 and Fred has $75

After Sally and Fred spending $125 and earning $50, respectively

Sally has

`\$375-\$125=\$250`

Fred has

`\$75+\$50=\$125`