Interest earned = 53.grandh01 wrote:A woman invested $1000, part at %5 and the rest at %6.
Her total investment with interest at the end of the year
was $1053. How much did she invest at %5.
1) 500
2) 600
3) 700
4) 900
5) 950
OA is C
We can plug in the answers, which represent the amount invested at 5% interest, with the balance invested at 6% interest.
Answer choice C: 700
.05(700) + .06(300) = 35+18 = 53.
Success!
The correct answer is C.
An alternate approach:
Combined interest rate = 53/1000 * 100 = 5.3%.
At its core, this is a MIXTURE problem: an interest rate of 5% is MIXED with an interest rate of 6% to earn a combined interest rate of 5.3%.
To determine (amount invested at 5%) : (amount invested at 6%), we can use alligation.
Step 1: Plot the 3 percentages on a number line, with the two starting percentages (5% and 6%) on the ends and the combined percentage (5.3%) in the middle.
5%-----------5.3%-------------------6%
Step 2: Calculate the distances between the percentages.
5%-----.3----5.3%---------.7---------6%
Step 3: Determine the ratio in the mixture.
The ratio in the mixture is the RECIPROCAL of the distances in red.
(amount invested at 5%) : (amount invested at 6%)= .7 : .3 = 700:300.
Thus, the amount invested at 5% interest = 700.
For two similar problems, check here:
https://www.beatthegmat.com/ratios-fract ... 15365.html
