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?
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.
Let's break down the problem step-by-step to write the equations:
1. Let's assume Cindy's initial amount of money as "x" dollars.
2. Elaine's initial amount of money can be represented as "y" dollars.
3. According to the problem, Cindy and Elaine have a total of $60.
This can be written as:
x + y = 60 Equation 1
4. Cindy gave Elaine $12, so her remaining amount will be (x - 12).
5. Elaine gave Cindy $10, so her remaining amount will be (y + 10).
6. Cindy would have three times as much money as Elaine after the exchange, which can be written as:
(x - 12) = 3(y + 10) Equation 2
To summarize, the equations we have are:
Equation 1: x + y = 60
Equation 2: x - 12 = 3(y + 10)
Now we can solve these equations simultaneously to find the initial amounts of money for Cindy and Elaine.