Question 1105373: Hi
Gilbert and germaine shared a sum of money.after germaine spent 70 dollars she had twice as muchas gilbert. Gilbert then received 300 dollars and he now had 3 times the amount of money germaine had at first. What was the total amount of money both of them had at the end.
Thanks
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let A = the amount of money that gilbert had to start with.
let B = the amount of money that germaine had to start with.
after germaine spent 70 dollars she had twice as much as gilbert.
B - 70 = 2A
gilbert then received 300 dollars and he now had 3 times the amount that germaine had at first.
A + 300 = 3 * B
from the first equation, solve for B to get B = 2A + 70.
in the second equation, replace B with 2A + 70 to get A + 300 = 3 * (2A + 70).
simplify to get A + 300 = 6A + 210.
subtract A from both sides of the equation and subtract 210 from both sides of the equation to get 300 - 210 = 6A - A.
simplify to get 90 = 5A.
solve for A to get A = 90/5 = 18.
since B = 2A + 70, then B = 2*18 + 70 = 106.
you have A = 18 and B = 106.
that's what gilbert and germaine had to start with.
B - 70 = 2A becomes 108 - 70 = 36 which results in 36 = 36 which is true.
A + 300 = 3B becomes 18 + 300 = 3*108 which results in 318 = 318 which is true.
the solution is confirmed to be good.
in the beginning, gilbert had A = 18 and germaine had B = 106
germaine then spent 70 dollars, so she had 108 - 70 = 36 dollars left.
gilbert then received 300 dollars, so he had 18 + 300 = 318 left.
at the end, gilbert and germaine had a total of 318 + 36 = 354 dollars.
that's your solution.
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