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avatar+231 

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?

 May 27, 2022
 #1
avatar+118146 
+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 :)

 May 27, 2022
 #2
avatar+231 
+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

 May 27, 2022

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