|
Question 1204068: Julie cashed a paycheck and repaid her brother $10 that she had borrowed from him. She then spent $30 on fuel for her car and half of the remaining money on a new tent for camping. She bought a pair of running shoes for $29.45 and had $17.75 left. How much did Julie receive when she cashed her paycheck?
Found 3 solutions by math_tutor2020, MathTherapy, ikleyn:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
x = her paycheck amount
x-10 = what she has left over after repaying her brother
x-10-30 = x-40 = left over amount after buying fuel
(1/2)(x-40) = 0.5x-20 = amount she has left after buying the tent
0.5x-20-29.45 = 0.5x-49.45 = amount she has left after buying the shoes
Set this equal to the stated value 17.75 so we can solve for x.
0.5x-49.45 = 17.75
0.5x = 17.75+49.45
0.5x = 67.20
2*0.5x = 2*67.20
x = $134.40 is the answer.
---------------------------------------
Checking the answer:
start = $134.40
repays brother = $134.40 - $10 = $124.40 left over
buys fuel = $124.40 - $30 = $94.40 left over
buys tent = (1/2)*($94.40) = $47.20 left over
buys shoes = $47.20 - $29.45 = $17.75 is what she'll have left over after purchasing all the items mentioned, and repaying her brother.
Answer is confirmed.
---------------------------------------
Another approach
She ended up with $17.75
Add on the price of the shoes to rewind the clock so she gets that money back.
17.75+29.45 = 47.20
Before buying the shoes, she would have $47.20
Double this to get $94.40 when we rewind the clock further back. This is the amount she would have just before buying the tent.
Then add on $30 to rewind further to get $124.40 to represent what she would have just before buying fuel.
Lastly, she'll take the $10 from her brother when rewinding the clock all the way back to the start point.
$124.40+$10 = $134.40
Basically we follow the "check" section shown above, but do so in reverse.
Any time we have a subtraction, the inverse would be addition. The inverse of halving is doubling.
This rewinding action is basically how we solve equations.
---------------------------------------
---------------------------------------
Answer: $134.40
Answer by MathTherapy(10552)  (Show Source):
Answer by ikleyn(52786)  (Show Source):
You can put this solution on YOUR website! .
Julie cashed a paycheck and repaid her brother $10 that she had borrowed from him.
She then spent $30 on fuel for her car and half of the remaining money on a new tent for camping.
She bought a pair of running shoes for $29.45 and had $17.75 left.
How much did Julie receive when she cashed her paycheck?
~~~~~~~~~~~~~~~~~~~
Tutor @MathTherapy mentioned very productive idea on use the backward method for this problem.
In this my post I will show how effectively this idea works.
So, let's stsart from the end.
Before Julie bought a pait of running choes, she had 17.75 + 29.45 = 47.20 dollars.
This amount was the "second half" of her "remaining" money - so, the "remaining" money amount
was 2*47.20 = 94.40 dollars .
Hence, her paycheck was $ 94.40 PLUS $30 PLUS $30, i.e. 94.40 + 10 + 30 = 134.40 dollars.
ANSWER. The paycheck was $134.40.
Solved.
The backward method in this problem works SO EFFECTIVELY,
that the problem can be solved MENTALLY in couple of lines without using equations.
|
|
|
| |
