SOLUTION: Tom spent 1/6 of his money and another $5 on a book. Then, he spent 2/5 of the remaining money and another $12 on some food. He had $24 left. How much money did he have at first

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Tom spent 1/6 of his money and another $5 on a book. Then, he spent 2/5 of the remaining money and another $12 on some food. He had $24 left. How much money did he have at first      Log On


   



Question 1185259: Tom spent 1/6 of his money and another $5 on a book. Then, he spent 2/5 of
the remaining money and another $12 on some food. He had $24 left. How
much money did he have at first?
Please help me teachers! I need big help on this.

Found 3 solutions by josgarithmetic, MathLover1, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
M, what money he started with

(1)
Has remaining 5M%2F6-5

and then
(2)
Has remaining %283%2F5%29%285M%2F6-5%29-12=24

%283%2F5%29%285M%2F6-5%29=36
5M%2F6=36%285%2F3%29%2B5
5M%2F6=60%2B5
M=%286%2F5%2965
highlight%28highlight%28M=78%29%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

he have at first $x
Tom spent 1%2F6 of his money and another $5 on a book.
x%2F6%2B5
the remaining money is x-%28x%2F6%2B5%29=%285+x%29%2F6+-+5

Then, he spent 2%2F5 of the remaining money and another $12 on some food.
%282%2F5%29%28%285+x%29%2F6+-+5%29%2B12=x%2F3+%2B+10

He had $24+left.
x=x%2F6%2B5%2Bx%2F3+%2B+10%2B24
x=78
How much money did he have at first?
check:
x%2F6=78%2F6=13
$5 on a book
total spent: 13%2B5=18
remaining money:78-18=60
he spent 2%2F5 of the remaining money which is $%282%2F5%2960=24
another $12 on some food
total spent: 13%2B5%2B24%2B12=+54
deduct from 78
78-54=24 which confirms he had $24+left

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Tom spent 1/6 of his money and another $5 on a book. Then, he spent 2/5 of
the remaining money and another $12 on some food. He had $24 left. How
much money did he have at first?
Please help me teachers! I need big help on this.
Let multiplicative factor be x
Spending 1%2F6 means that there are 6 parts, so when 1 part (x) is spent, 5%2F6 or 5 parts, or 5x remains
As an additional $5 was spent, remainder is 5x - 5
Spending 2%2F5 of remainder and another $12 means that matrix%281%2C3%2C+3%2F5%2C+of%2C+%285x+-+5%29+-+12%29 remains
Now, as $24 remains in the end, we get:
With original number of parts being 6, original amount = highlight_green%28matrix%281%2C3%2C+6%2813%29%2C+%22=%22%2C+%22%2478%22%29%29