Problem Solving

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

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

Interest earned = 53.

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

For this one you can try and plug in the options.

I always start with the middle one so hit the jackpot here.

Say $700 was at 5%

So at the end of the year the woman will get = 735

Remaining $300 was at 6%. So end of the year the woman will get = 318.


Add the two and you will get $ 1053.

So answer is $ 700. You can try this for all options and check.

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

Thous options work well. For me I like algebraic approaches (everyone's different). For an algebraic approach:

Original Amount =1000
New Amount = 1053
So there was 53 in interest (1053-1000)
Now set up an unknown variable. We want to know how much earned 5%, so lets say that is x
Our Equation:
.05x+.06(1000-x) = 53. Do you understand how I came up with this equation?
-.01x=60=53
-.01x=-7
x=700
The correct answer is C

Assume she invested x$ at 5% and (1000 - x)$ at 6%. It then follows that:

0.05(x) + 0.06(1000 - x) = 53

60 - 0.01(x) = 53

x = $700 at 5%.