Algebra Word Problem

Question

Joe got money for his birthday. He spent $5 on candy, $13 on a new shirt and half of the remaining amount on a new sweater. How much did Joe get for his birthday if he is left with $16?

Answer 1

Money from Birthday, minus candy, minus shirt, minus sweater = money left over.

Let M be the amount of money he got on his birthday.

M - 5 - 13 - (M - 18)/2 = 16

M - 18 - (M - 18)/2 = 16

Multiply both sides by 2

2M - 36 - (M - 18) = 32

2M - 36 - M + 18 = 32

M - 18 = 32

M = 32 + 18 = 50

Joe got $50 for his birthday.

Check:

Money - candy - shirt

50 - 5 - 13 = 32

After Joe bought candy and a shirt, he had $32 left. Half of that was used to buy a sweater, so the sweater cost 32/2 = 16 dollars.

Money - candy - shirt - sweater = money left over

50 - 5 - 13 - 16 = 16

Hope this helps!

Answer 2

Half of the remaining amount on a new sweater - and he's left with $16... therefore, the sweater cost $16.

Therefore, Joe got $16 + $16 + $13 + $5 for his birthday.