fitzpratik wrote:
A total of $1200 is deposited in two savings account for one year, part at 5% and the remainder at 7%. If $72 was earned in interest, how much was deposited at 5%?
A. 410
B. 520
C. 600
D. 650
E. 760
Source: Nova -GMAT
AlgebraWe have two different amounts invested at different interest rates.
We can treat this question as we would a mixture problem.
Define one amount in terms of the other.
\(x\) = the amount invested at 5%
\(y\) = the amount invested at 7%
\(x +y=$1200\)
\(y=(1200-x)\)
The
sum of the interest earned on each part is \($72\)
\((.05)(x)+(.07)(y)=72\)
\((.05)(x)+(.07)(1200-x)=72\)
Multiply all terms by \(100\)
\(5x+(7)(1200-x)=7200\)
\(5x+8,400-7x=7200\)
\(1,200=2x\)
\(x=600\)
Answer C
Use the answer choicesStart with C to get a benchmark.*
C) 600 = the amount invested at 5%
The total amount invested is $1,200
The other portion invested at 7% also = $600
Interest earned by $600 at 5%:
\($600 * \frac{5}{100}=$30\)
Interest earned by $600 at 7%
\(($600*\frac{7}{100})=$42\)
Total interest earned? $72
$30 + $42 = $72
That's correct.
Answer C
**Using a benchmark
If C is too great, eliminate D and E. Both are greater than C.
If C is too small, eliminate A and B. Both are smaller than C.
Suppose we had started with E) $760
Interest earned by $760 at 5% ?
10% would be $38. 5% is half that: $38
Other portion = $(1,200 - 760) = $440
Interest earned? $440 * \(\frac{7}{100}\)= ($4.40 * 7) = $30.80
Total interest? $38 + $30.80 = $60.80
Actual total interest earned? $72.00. The theoretical $60.80 earned is a lot less than $72.
$760 at 5% is too great an amount—too much of the original $1,200.
We need the higher interest rate, 7%, to earn more. Make the 7% portion's base amount greater.
To do so, decrease the 5% base amount. Try (C).
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