Question 70453: (I tried to help my daughter with this problem using her new system of diagrams/boxes. It's from a class handout. I'm afraid it's been too long since my last algebra class for me to help out. Thanks.)
Dennis had a certain sum of money and he spent $100 on books. He gave 2/3
of the remainder to his mother and saved the rest. If he saved 3/10 of the
total amount he had at first, how much did he give to his mother?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Dennis had a certain sum of money and he spent $100 on books. He gave 2/3
of the remainder to his mother and saved the rest. If he saved 3/10 of the
total amount he had at first, how much did he give to his mother?
:
I'm not sure about a diagram or box for this but here's how I would do it:
:
Original amt = x
:
After buying book = (x-100)
;
Gift to Mama = (2/3)(x-100)
:
There remaineth = (1/3)(x-100)
:
Problems states .3x was saved, hence a simple equation:
:
(1/3)(x-100) = .3x
:
Get rid of denominator, multiply equation by 3
1(x - 100) = 3(.3x)
x - 100 = .9x
x - .9x = 100
.1x = 100
x = 100/.1
x = $1000 is original amt
:
Gift to mama; 2/3(1000-100) = (2/3)900 = $600
:
:
Check:
book + mama + savings = 1000
100 + 600 + 300 = 1000
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