SOLUTION: Henry spent 1/4 of his money and an additional $3 on a number of DVDs. He then spent 3/5 of the remaining money and an additional $6 on a number of batteries. Given that he was lef

Question 1184436: Henry spent 1/4 of his money and an additional $3 on a number of DVDs. He then spent 3/5 of the remaining money and an additional $6 on a number of batteries. Given that he was left with $24, how much money did Henry have at first?
Answer by ikleyn(52798) (Show Source): You can put this solution on YOUR website!
.
Henry spent 1/4 of his money and an additional $3 on a number of DVDs.
He then spent 3/5 of the remaining money and an additional $6 on a number of batteries.
Given that he was left with $24, how much money did Henry have at first?
~~~~~~~~~~~~~~~~~

It is a nice problem to be solved backward and explained accordingly.

First, let x be the remainder money amount after buying a number of DVDs.


Then for this amount of money you have this equation

    x -  = 24.     (1)


To solve it, multiply everything in equation (1) by 5  to get

    5x - (3x + 30) = 24*5

    5x - 3x        = 24*5 + 30

       2x          = 120 + 30 = 150

        x                     = 150/2 = 75.


Thus you found that after buying a number of DVDs, the remainder was 75 dollars.


OK.     It gives you  NEXT EQUATION from the first part of the problem 

    M -  = 75    (2)


where M is the unknown money amount Henry had at first.


From this equation, you get

     = 75 + 3 = 78,

        M    =  = 26*4 = 104.


ANSWER.  At first,  Henry had $104.

Solved and thoroughly explained.

Check my answer on your own.

RELATED QUESTIONS
Please support with explanation , thk Bill spent 1/6 of his money and an additional $11... (answered by Theo,greenestamps)

Hi Jason spent 1/4 of his money and an extra $10 on some books. He the spent 2/5 of the... (answered by greenestamps,josgarithmetic,Solver92311,MathTherapy)

Tom worked for a week from Monday to Friday and was paid $7 per hour. He used 3/5 of his (answered by greenestamps)

Max spent 1/4 of his money and an additional $ 60 on a present for his best friend.He... (answered by MathTherapy)

Aloysius had some money at first. He spent $360 on a suit. He then spent 1/7 of his... (answered by josgarithmetic,ikleyn,greenestamps,MathTherapy)

Nelson had some money. He spent $124.50 on a shirt and 3/8 of the remaining money on some (answered by josgarithmetic)

I cannot understand this answer, please help. Thank you. Justin spent 3/10 of his money... (answered by Theo,ikleyn)

John had rs 4500.He spent 1/3 of his money on a table and the remaining on 5 chairs. how... (answered by FrankM)

Mylan spent $3 on a magazine. He spent half of his remaining money on a video. He then... (answered by Edwin McCravy,unlockmath)