Let's call the amount of money Cindy had originally "C" and the amount of money Elaine had originally "E".
From the problem, we know:
C + E = 60 (since they have $60 altogether)
If Cindy gave Elaine $12, she would have C - 12, and Elaine would have E + 12.
If Elaine gave Cindy $10, she would have E - 10 and Cindy would have C + 10.
And we also know that if Cindy gave Elaine $12 and Elaine gave Cindy $10, Cindy would have three times as much money as Elaine. In other words:
C - 12 = 3(E + 12)
Now we have two equations:
C + E = 60
C - 12 = 3(E + 12)
We can use substitution or elimination to solve for either C or E. Let's use substitution.
From the first equation, we can solve for C:
C = 60 - E
Now we can substitute that expression for C into the second equation:
60 - E - 12 = 3(E + 12)
Simplifying:
48 - E = 3E + 36
4E = 12
E = 3
So Elaine originally had $3.
We can use the equation C + E = 60 to find out how much Cindy had originally:
C + 3 = 60
C = 57
So Cindy originally had $57.
Therefore, Cindy originally had $57 and Elaine originally had $3.
Write an equation with variable to solve each problem.
Cindy & Elaine and $60 altogether. If Cindy gave Elaine $12 and Elaine gave Cindy $10, Cindy would have three times as many money as Elaine. How much money did each of them have first?
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