Jackson invested #300,000, divinding it all unequally...

Hi swerve,

We're told that Jackson invested $300,000 between Account P and Account Q and at the end of one year, Account P had earned 12% interest and Account Q had earned 25% interest. If Jackson earned a total of $60,000 in interest between the two accounts, we're asked which of the following is APPROXIMATELY the amount he put in Account P. This question can be solved with 'system Algebra' or by TESTing THE ANSWERS.

Let's TEST Answer B: $120,000

IF.... $120,000 was invested at 12% interest, then the interest for this Account would be (.12)($120,000) = $14,400
The remaining $180,000 was invested at 25% interest, so the interest for this Account would be (.25)($180,000) = $45,000
Total interest generated = $14,400 + $45,000 = $59,400

This is fairly close to $60,000, but not close enough that this would be the answer. To INCREASE the amount of total interest, we need to invest MORE money in Account Q - and that means there would be LESS money in Account P. We need an investment that is less than $120,000 and there's only one answer left that 'fits.'

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

swerve wrote:Jackson invested $300,000 dividing it all unequally between Account P and Account Q. At the end of the year, it turned out that Account P had earned 12% interest and Account Q had earned 25% interest. If Jackson earned a total of $60,000 in interest between the two accounts, which of the following is approximately the amount he put in Account P?

A. $115,384
B. $120,000
C. $121,072
D. $124,129
E. $130,000

We can let P = the amount invested in P and Q = the amount invested in Q and create the equations:

P + Q = 300,000

Q = 300,000 - P

and

0.12P + 0.25Q = 60,000

12P + 25Q = 6,000,000

Substituting 300,000 - P for Q, we have:

12P + 25(300,000 - P) = 6,000,000

12P + 7,500,000 - 25P = 6,000,000

1,500,000 = 13P

115,384 ≈ P

Answer: A