SOLUTION: angela has more money than carla. If angela gave carla 20$, they would have the same amount. If carla gave angela 22$, angela would have twice the amount as carla. How much does ea

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Question 1204637: angela has more money than carla. If angela gave carla 20$, they would have the same amount. If carla gave angela 22$, angela would have twice the amount as carla. How much does each person have? Form and use equations to find your answer.
Found 3 solutions by ikleyn, mananth, greenestamps:
Answer by ikleyn(52784)   (Show Source): You can put this solution on YOUR website!
.
angela has more money than carla. If angela gave carla 20$, they would have the same amount.
If carla gave angela 22$, angela would have twice the amount as carla.
How much does each person have? Form and use equations to find your answer.
~~~~~~~~~~~~~~~~~~~~~~ 

First equation is

    A - 20 = C + 20.      (1)


Second equation is

    A + 22 = 2*(C-22).    (2)


To solve, subtract equation (1) from equation (2).  You will get

    22 + 20 = C - 44 - 20,

or

    22 + 20 + 44 + 20 = C

    C = 106.


Thus, Carla has 106 dollars;  Angela has A = C + 20 + 20 = 146 dollars.    ANSWER


You may check on your own, that the answer satisfies the given conditions.

Solved.



Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
angela has more money than carla. If angela gave carla 20$, they would have the same amount. If carla gave angela 22$, angela would have twice the amount as carla. How much does each person have? Form and use equations to find your answer.
Let angela have $x
Carla have $y
If angela gave carla 20$, they would have the same amount.
x-20=y+20
x-y=40----------------------(1)
If carla gave angela 22$, angela would have twice the amount as carla
y-22 = (x+22)= 2(y-22)
x+22=2y-44
x-2y= -66--------------------(2)
Multiply (1) by -2 and add the equation to(2)
-2x+2y=-80
x-2y= -66
-x= -146
x=146
146-y =40
y=106

Therefore, Angela has $146, and Carla has $106.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


A different setup for solving the problem. Not better, just different....

If Angela gave Carla $20, they would each have the same amount.

Let x be the amount they would each have if Angela gave Carla $20.

Then the amount Angela starts with is x+20, and the amount Carla starts with is x-20.

So if Carla gave Angela $22, the amount Angela would have would be x+20+22 = x+42, and the amount Carla would have would be x-20-22 = x-42. In that case, Angela would have twice as much as Carla:





So the amounts each of them has is...

ANSWERS:
Angela: x+20 = $146
Carla: x-20 = $106

Note that by looking for a different way to set up the problem, we can solve the problem using a single variable. That often makes the work easier.... (But not always)
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