Question

Elliot spent 3/7 of his money on some comics. He spent 1/4

of the remaining money on a pack of cards.
a) What fraction of Elliot's money has he left?
b) If he has $6 left, how much money did Elliot have at first?

Answer 1

a) 3/7

b) $14

Explanation:

let the total of his Money be x

on some comics = 3/7 of x

`(3)/(7) * x \: = (3x)/(7)`

remaining money = x - 3x/7

`x - (3x)/(7) = (7x - 3x)/(7) = (4x)/(7)`

on a pack of cards = 1/4 of 4x/7

`(1)/(4) * (4x)/(7) = (4x)/(28) = (x)/(7)`

a) left fraction = total money - all spent money

note that; all spent money = money spent on some comics and pack of cards

`x - ( (3x)/(7) + (x)/(7) )`

`x - ( (3x + x )/(7) )`

`x - (4x)/(7) = (7x - 4x)/(7) = (3x)/(7)`

left fraction = 3/7 of the money

b) left money = 3x/7

but since left money is $6

therefore, $6 = 3x/7

multiply both sides by 7

`6 * 7 = (3x)/(7) * 7`

42= 3x

divide both sides by 3

x = 42/3

x = 14

total money = $14