# Mark is throwing his son Stewart a surprise birthday party but he.........is out of money, how much did Mark start with?

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Mark is throwing his son Stewart a surprise birthday party but he has limited funds.

He spent half of his money plus \$2.00 on the cake.

Half of what was left plus \$2.00 was spent on balloons and decorations.

Then he spent half of what he had left plus \$1.00 on candy.

Now he is out of money, how much did Mark start with?

posted Jan 3

+1 vote

Let X be the initial amount
Money spent on cake = X/2 + 2 ------ 1
Money spent on balloon = (X - (X/2 + 2))/2 + 2
= (X/2 - 2)/2 + 2
= X/4 + 1 -------- 2
Money spent on candy = (X - (X/2 + 2) - (X/4 + 1))/2 + 1
= (X/4 - 3)/2 + 1
= X/8 - 1/2. ---------- 3

As per the question
X = 1 + 2 + 3.
X = (X/2 + 2) + (X/4 + 1) + (X/8 - 1/2)
X = 7X/8 - 5/2
X = 20 ie, \$20.

If he started with \$20, he spends 1/2, or \$10, plus \$2 on the cake, leaving him with \$8. Then he spends 1/2,\$4, plus \$2 on balloons and decorations, leaving him with \$2. Then he spends 1/2, \$1 , plus the last \$1 on candy. Now he has \$0.
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