SOLUTION: Sam saved his money until he had $10 000 to invest. He invested x dollars into a certificate of deposit with an annual interest of 2.0%, and the remaining y dollars into a mutual f

Question 1163118: Sam saved his money until he had $10 000 to invest. He invested x dollars into a certificate of deposit with an annual interest of 2.0%, and the remaining y dollars into a mutual fund with an annual interest rate of 1.5%. If his total interest earned from both accounts after one year was $193, which of the following is the value of y?
Found 3 solutions by Theo, MathTherapy, greenestamps:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
x = the amount invested at 2%.
y = the amount invested at 1.5%
x + y = 10,000
.02x + .015y = 193
multiply both sides of the first equation by .02 and leave the second equation as is to get:
.02x + .02y = 200
.02x + .015y = 193
subtract the second equation from the first to get:
.005y = 7
solve for y to get:
y = 1400
that makes x = 10,000 - 1400 = 8600.
you have:
x = 8600
y = 1400
confirm solution is correct as shown below.
x + y = 8600 + 1400 = 10,000 (correct)
.02x+ .015y = .02 * 8600 + .015 * 1400 = 172 + 21 = 193 (correct)
solution is confirmed to be correct.
solution is the value of y is 1400.

Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

Sam saved his money until he had $10 000 to invest. He invested x dollars into a certificate of deposit with an annual interest of 2.0%, and the remaining y dollars into a mutual fund with an annual interest rate of 1.5%. If his total interest earned from both accounts after one year was $193, which of the following is the value of y?

I thought that "which of the following" would PRECEDE a list of choices. Why aren't those choices listed?
With "y" being the amount invested at 1.5%, amount invested at 2%/x = 10,000 - y
We then get: .02(10,000 - y) + .015y = 193
200 - .02y + .015y = 193
- .02y + .015y = 193 - 200
- .005y = - 7
Amount invested at 1.5%, or
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

Here is a quick and easy way to solve a "mixture" problem like this if a formal algebraic solution is not required.

All $10,000 invested at 1.5% would yield $150 interest; all at 2% would yield $200 interest.

The actual interest, $193, is 43/50 of the way from $150 to $200. (Picture the three numbers on a number line -- 150 to 200 is a difference of 50; 150 to 193 is a difference of 43.)

That means 43/50 of the total was invested at 2%; so 7/50 of the total was invested at 1.5%.

ANSWER: The amount invested at 1.5% was 7/50 of $10,000, which is $1400.

CHECK:
.015(1400)+.02(8600) = 21+172 = 193

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