You have no money in your wallet, so your mother gives you some money to go to t

Question

You have no money in your wallet, so your mother gives you some money to go to the mall to hang out with your friends. You need your caffeine fix, so y o u first head over to Tully's and spend 1/21 of your money on a Latte. You then head over to R.E.I. and sp end 1/8 of your remaining money on a pair of snowboarding socks. Next, you go over to Best Buy and waste 1/5 of your remaining money on the Lindsay Lohan CD. You then find a cool t - shirt that says "5 out of 4 people can"t do fractions." You find this amusing, so you spend 2/7 of your remaining money on this shirt. Finally, you and your friends are hungry. You spend 3/4 of the remaining money by treating your friends to lunch at Chili's. You finally go home and give your mom $10 back. How much money did you start out with and how much did each item cost ?

Explanation / Answer

Let's assume that I started with $'x'

Money left after buying latte = (1 - 1/21)*x = 20x/21

Money left after buying snowboarding socks = ( 1 - 1/8) * (20x/21) = 140x / 168 = 5x/6

Money left after buying CD = ( 1 - 1/5) * 5x/6 = 2x/3

Money left after buying shirt = ( 1 - 2/7) * 2x/3 = 10x/21

Money left after treating = ( 1 - 3/4) * 10x/21 = 10x/84

As per question, 10x/84 = 10

x = 84, which means I started with 84 $

Latte = 1/21 * 84 = $4

Snowboarding socks = 1/8 * (84-4) = $10

CD = 1/5 * (84 -4 -10) = $14

Shirt = 2/7 * ( 84 -4 -10 -14) = $16

Treat = 3/4 * ( 84 - 4 - 10 -14 -16) = 30

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