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

Answer:

a) 3/7

b) $14

Step-by-step explanation:

let the total of his Money be x

on some comics = 3/7 of x

$\frac{3}{7} \times x \: = \frac{3x}{7}$

remaining money = x - 3x/7

$x - \frac{3x}{7} = \frac{7x - 3x}{7} = \frac{4x}{7}$

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

$\frac{1}{4} \times \frac{4x}{7} = \frac{4x}{28} = \frac{x}{7}$

a) left fraction = total money - all spent money

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

$x - ( \frac{3x}{7} + \frac{x}{7} )$

$x - ( \frac{3x + x }{7} )$

$x - \frac{4x}{7} = \frac{7x - 4x}{7} = \frac{3x}{7}$

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

$6 \times 7 = \frac{3x}{7} \times 7$

42= 3x

divide both sides by 3

x = 42/3

x = 14

total money = $14