The ratio of Ben's money to John's money was 9:4. After Ben spent $63 on books, the ratio became 1:2. How much more money did John have than Ben then?

Slimesewer May 27, 2022

#1**+1 **

Initially Ben had 9x dollars and John has 4x dollars.

Ben spends $63 so now Ben has 9x-63 dollars and John still has 4x dolllars.

This is in the ration 1:2

so

\(\frac{9x-63}{1}=\frac{4x}{2}\\ 9x-63=2x\\ 7x=63\\ x=9\)

You can finish it :)

Melody May 27, 2022

#2**+1 **

Let Ben's money = 2x

and John's money = y

Therefore x:y = 9:4

i.e x/y = 9/4 Cross multiply

4x = 9y -- (1)

After Ben spends $63

Ben's money becomes x - 63

x - 63 : y = 1:2

(x - 63)/y = 1/2

2(x - 63) = y

2x - 126 = y

Input value of y in eq (1)

4x = 9(2x - 126)

4x = 18x - 1134

1134 = 18x - 4x

1134 = 14x

1134/14 = x x = 89

Since 4x = 9y

4 (81) = 9y

324 = 9y

324/9 = y

36 = y

Ben's money = $81 and

John's money = $36

After Ben spends $63 his money

becomes $81 - $63 = $18

John becomes $(36 - 18) more = $18 more

Slimesewer May 27, 2022