Question

Charlie says to Mia, "If you give me $9.00, we will have an equal amount of money." Mia responds, "That may be true, but if you give me $9.00 instead, I will have twice as much money as you." How much money did Charlie and Mia each have in the beginning?

Answer 1

• Charlie: $45
• Mia: $63

Explanation:

The two descriptions can be written as two equations. We can let "m" and "c" represent the amounts that Mia and Charlie have to begin with. Then ...

m -9 = c+9 . . . . . equal amounts if Mia gives Charlie $9

m +9 = 2(c -9) . . Mia has double if Charlies gives Mia $9

Subtracting the first equation from the second gives ...

(m +9) -(m -9) = (2(c -9)) -(c +9)

18 = c -27 . . . simplify

45 = c . . . . . . add 27

Substituting into the first equation, we have ...

m -9 = 45 +9

m = 63 . . . . . . . add 9 and simplify

Charlie and Mia started with $45 and $63, respectively.