Hannah and Ethan went to the mall with an equal amount of mo

Hannah and Ethan went to the mall with an equal amount of money to buy their mother a birthday present. Hannah purchased a $36 scarf and Ethan bought his mother a jewelry box for $47. After the purchases, Ethan had 3/4 of the money that Hannah has remaining. How much money did each start with before their purchase?

Solution

Given that

Hannah and Ethan having an equal amount of money

Let an equal amount of money = $x

Hannah purchased a scarf = $36

  Hannah had the remaining money = x - $36

Ethan bought a jewelry box = $47.

  Ethan had the remaining money = x - $47

After the purchases, Ethan had 3/4 of the money that Hannah has remaing

i.e x - $47 = (3/4) ( x - $36 )

4( x - $47 ) = 3 ( x - $36 )

4x - $188 = $3x - $108

4x - $3x = -$108 + $188

x = $80

Equal amount of money x = $80

Hence,

  Hannah and Ethan start with the money before purchase = $80