a little Math help, please

[majimikate]

This is my son's problem of the week. Both he and I have looked at it several times and can't seem to figure out how to properly set up the equation to solve it. At one point we had 2 variables, (that was wrong), but no matter how we have both tried, we keep coming up with an equation that doesn't work! Any and all help would be greatly appreciated!

Here it is:

Matt put $15 of his paycheck in savings. Then he spent one half of what was left on clothes. He paid $24 for a concert ticket and later spent one half of what was then left on a book. When he got home, he had $14 left. What was the amount of Matt's paycheck?
It seems I should be able to work backwards from the $14, but I can't get it right! SO frustrating!!! Math whizzes, please help if you can! Thank you!

Chris

 

[FredinFL]

Not enough?

 

[dejr_8]

Pay = $119

$15 went into savings leaving $104
$52 was spent on clothes (1/2 of what was left)
bought a concert ticket for $24 leaving $28 dollars
1/2 of the $28 dollars ($14) was used to buy a book leaving him with $14.

 

[MickeyMickey]

Pay = $119

$15 went into savings leaving $104
$52 was spent on clothes (1/2 of what was left)
bought a concert ticket for $24 leaving $28 dollars
1/2 of the $28 dollars ($14) was used to buy a book leaving him with $14.

What she said

 

[dejr_8]

In equation form

Pay = 2*(2*$14 + $24) + $15

 

[ilovemk76]

Matt put $15 of his paycheck in savings. Then he spent one half of what was left on clothes. He paid $24 for a concert ticket and later spent one half of what was then left on a book. When he got home, he had $14 left. What was the amount of Matt's paycheck?

Y = Total amount of the paycheck
X = The amount left over after the savings deposit.

Y = X + 15

1/2X = Spent on clothes
24 = Spent on a concert ticket


At this time Matt has X - (X/2) - 24 dollars left [X/2 - 24]

1/2(X/2 - 24) = Spent on a book [X/4-12]

14 = What he had left. This is also what the book cost.

So 14 = X/4 - 12
26 = X/4
X = 104

Y = 104 + 15 = 119

Savings - $15
Clothes cost - $52
Tickets cost - $24
Book cost - $14
Left over - $14

 

[majimikate]

Excellent!! Thank you so much, makes perfect sense, I was almost there, kept screwing up on the clothing purchase at $56 instead of $52...but I get it, I could explain it to my son, and now he gets it too, thank you all so much!

Chris