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19 Feb 2018, 22:24
1
00:00

Difficulty:

45% (medium)

Question Stats:

68% (02:05) correct 32% (02:22) wrong based on 54 sessions

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Mr. Williams invested a total of $12,000 for a one-year period. Part of the money was invested at 5% simple interest, and the rest was invested at 12% simple interest. If he earned a total of$880 in interest for the year, how much of the money was invested at 12%?

(A) $1,920 (B)$4,000

(C) $4,800 (D)$7,200

(E) $8,000 _________________ Senior Manager Joined: 31 May 2017 Posts: 320 Re: Mr. Williams invested a total of$12,000 for a one-year period. Part  [#permalink]

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19 Feb 2018, 22:41
1
We can solve this question quickly by plugging in values and eliminating wrong answers straight away.

Step 1: Total interest rate accumulated is $880. Lets take a random split say$6000 each. Now if you calculate $6000 at 12% interest is$720 and at 5% is 300 which gives us $920. So part of amount invested at less than 12% is definitely less than$6000. Eliminate Option D and E. Actually we can eliminate option A without much calculation as well.

So we are left with option B and C.

Step 2:
Next lets take next highest value , $4800 ,which at 12% will yield$576 and rest of $7200 at 5% will yield 360.$576+$360 >$880.

So we are left with option B - $4000 - which @12% gives 480 and balance$8000 at 5% gives 400 - $480 +$400 = $880. Ans: B _________________ Please give kudos if it helps Resources | | | | | Senior SC Moderator Joined: 22 May 2016 Posts: 2204 Mr. Williams invested a total of$12,000 for a one-year period. Part  [#permalink]

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24 Feb 2018, 00:12
1
1
Bunuel wrote:
Mr. Williams invested a total of $12,000 for a one-year period. Part of the money was invested at 5% simple interest, and the rest was invested at 12% simple interest. If he earned a total of$880 in interest for the year, how much of the money was invested at 12%?

(A) $1,920 (B)$4,000

(C) $4,800 (D)$7,200

(E) $8,000 Try a weighted average approach, similar to that in mixture problems. Interest, as a percent, is like concentration. Let x = amount in dollars invested at 5% (below, equivalent to "weight") Let y = amount in dollars invested at 12% (below, equivalent to "weight") $$x + y = 12,000$$ $$x = 12,000 - y$$ $$(Rate_1)(Weight_1) + (R_2)(W_2)$$ = Total Interest $$.05x + .12y = 880$$ Substitute $$x = (12,000 - y)$$ $$.05(12,000 - y) + .12y = 880$$ $$600 - .05y + .12y = 880$$ $$.07y = 280$$ $$y = \frac{280}{.07}=\frac{28,000}{7}=4,000$$ Answer B Mr. Williams invested a total of$12,000 for a one-year period. Part &nbs [#permalink] 24 Feb 2018, 00:12
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# Mr. Williams invested a total of \$12,000 for a one-year period. Part

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