SOLUTION: gavin spent 3/5 of his money on the first week and 1/3 of the remainder on the second week. he spent $110 dollars altogether. how much money did he have left?

Question 1206653: gavin spent 3/5 of his money on the first week and 1/3 of the remainder on the second week. he spent $110 dollars altogether. how much money did he have left?
Found 3 solutions by MathLover1, math_tutor2020, josgarithmetic:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

gavin spent of his money (total amount is ) on the first week

is the remainder
and of the remainder on the second week

he spent $ dollars altogether

total amount is $
first week he spent:
second week he spent:
how much money did he have left:
$

Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

Draw 5 rectangles placed side by side.
Shade 3 of them to represent Gavin spending 3/5 of his initial money.
Refer to figure 1 shown below.
The remaining 2/5 is what he has leftover (before spending the next round of money).

Then draw in 2 horizontal lines to divide those 5 blocks into 3*5 = 15 blocks. Shade the top row, of the 3 rows, to represent Gavin spending 1/3 of what he has left.
Refer to figure 2.

How many small blocks are shaded?
There's 3 full columns shaded in the first round.
Each column has 3 small blocks so that's 3*3 = 9 small blocks so far.
Then we have 2 more small blocks when Gavin moves to the next round of spending.
There are 9+2 = 11 small blocks shaded out of 15 total.

That means Gavin spent 11/15 of his initial money.
Another way to reach this fraction is to compute 3/5 + (1/3)*(2/5)

x = how much money he starts with
(11/15)*x = 110 = how much money in total is spent
x = 110*(15/11)
x = 150
Gavin started with $150 and spent $110.
He has $40 left since 150-110 = 40.

Alternative route:
He spent 11/15 of his money and saves the remaining 4/15
(4/15)*150 = 40

Answer: $40

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
first week start, M
spent
still has

second week start,
spent
spent

Amount spent,

-----------What had before any spending

, what he had remaining after the two spendings
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