Problem Solving

LUANDATO 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) $260

The OA is D.

Can any expert help me with this PS question please? How can I solve it? Thanks.

Let Al have $a and Elliot have $e in their respective bank accounts.

Since we know that if Al's account were to increase by 10% and Eliot's account were to increase by 20% (More than 10%), then Al would have exactly $22 more than Eliot in his account, it means that Al has more money in his account than Elliot has. Thus, a > e.

Since the difference between their two accounts is 1/12 of the sum of their two accounts, we have,

a - e = 1/12 of (a + e); we know that a > e

=> a = 13a/11 ---(1)

Since 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, we have,

110% of a - 120% of e = 22

=> 1.1a - 1.2e = 22 ---(2)

By plugging in the value of a from (1) in equation (2), we get,

1.1a - 1.2e = 22 => 1.1(1.3/11)e - 1.2e = 22 => 0.1e = 22 => [spoiler]e = $220[/spoiler]

The correct answer: D

Hope this helps!

-Jay

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