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

Question

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?

Answer 1

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.

Answer 2

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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