mikemcgarry wrote:
Right now, Al and Eliot have bank accounts, and Al has more money than Eliot. The difference between their two accounts is 1/12 of the sum of their two accounts. If Al’s account were to increase by 10% and Eliot’s account were to increase by 20%, then Al would have exactly $22 more than Eliot in his account. How much money does Eliot have in his account right now?
(A) $110
(B) $120
(C) $180
(D) $220
(E) $260Word problems can be tricky, and one tricky issue is assigning variables. For a discussion of some guidelines, as well as the OE for this particular question, see:
Intro to GMAT Word Problems, Part 2: Assigning VariablesMike
Lets assume Al have amount A in his bank account and Eliot's bank account got E amount. We can form an equation from the first condition.
A-E = 1/12*(A+E) ==> 11A = 13E ------------ (1)
Second condition gives two different amounts, Al's amount = 1.1A and Eliot's amount = 1.2E
1.1A = 22 + 1.2E ==> 11A =220 +12E -------(2)
Substituting (1) in (2):
13E = 220+12E ==>
E = 220
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