SOLUTION: 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 amoun

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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