Question

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?

Answer 1

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.