SOLUTION: DENNIS SAVINGS WAS 2/5 MORE THAN JULIA. AFTER DENNIS HAD GIVEN $500 TO JULIA HE HAD 1/5 OF JULIAS MONEY. FIND THEIR TOTAL SAVINGS?

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Question 175356: DENNIS SAVINGS WAS 2/5 MORE THAN JULIA. AFTER DENNIS HAD GIVEN $500 TO JULIA HE HAD 1/5 OF JULIAS MONEY. FIND THEIR TOTAL SAVINGS?

Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website!
let x = what dennis has now.
let y = what julia has now.
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dennis savings is 2/5 more than what julia has.
x = y + 2y/5 = 7y/5
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after dennis gives 500 to julia, he has 1/5 of what julia has after she receives the 500.
x - 500 = (y + 500)/5
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you have 2 equations that you need to solve simultaneously.
they are:
x = 7y/5 (first equation)
x-500 = (y+500)/5 (second equation)
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since you already have x = 7y/5, you can solve by substituting 7y/5 for x in the second equation.
you get:
7y/5 - 500 = (y+500)/5
multiply each side of the equation by 5 to clear the fractions and get:
7y - 2500 = y + 500
subtract y from both sides of the equation to get:
6y - 2500 = 500
add 2500 to both sides of the equation to get:
6y = 3000
divide both sides of the equation by 6 to get:
y = 500
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substitute 500 for y in the first equation to get:
x = 7*(500)/5 = 7*100 = 700
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you have:
x = 700
y = 500
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this means that:
dennis has 700
julia has 500
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first part of problem states that dennis had 2/5 more than what julia had.
700 = 500 + 2/5 * 500 = 500 + 200 = 700
this part is good.
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second part of problem states that dennis has 1/5 what julia has after he gives her 500.
700 - 500 = 200 = 1/5 * (500 + 500) = 1/5 * (1000) = 200
this part is good.
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answer has been checked and is good.
dennis had 700 and julia had 500 before dennis gave her the 500.
dennis had 200 and julia had 1000 after dennis gave her the 500.
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