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prealgebra intermediate
Problem
Al, Betty, and Clare split among them to be invested in different ways. Each begins with a different amount. At the end of one year, they have a total of dollars. Betty and Clare have both doubled their money, whereas Al has managed to lose dollars. What was Al's original portion?
(A)
(B)
(C)
(D)
Solution
For this problem, we will have to write a three-variable equation, but not necessarily solve it. Let and represent the original portions of Al, Betty, and Clare, respectively. At the end of one year, they each have and . From this, we can write two equations, marked by (1) and (2). (Equations (1) and (2) are derived from each equation above them.) Since all we need to find is subtract the second equation from the first equation to get Al's original portion was .
Final answer
C