SOLUTION: You invested money in two funds. Last year, the first fund paid a dividend of 9% and the second a dividend of 3%, and you received a total $1,047. This year, the fund paid a 10% di

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: You invested money in two funds. Last year, the first fund paid a dividend of 9% and the second a dividend of 3%, and you received a total $1,047. This year, the fund paid a 10% di      Log On


   

Question 270613: You invested money in two funds. Last year, the first fund paid a dividend of 9% and the second a dividend of 3%, and you received a total $1,047. This year, the fund paid a 10% dividend and the second only 1% and you received a total of $826. How much money did you invest in each fund?



I am so confused witth this problem! Can someone please help me?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x = amount invested in the first fund.
let y = the invested in the second fund.

Last year the dividends you received were 1047.

Part of that was from the first fund that earned 9% and part of that was from the second fund that earned 3%.

The equation for the dividends earned last year would be:

.09*x + .03*y = 1047.

This year the dividends you received were 826.

Part of that was from the first fund that earned 10% and part of that was from the second fund that earned 1%.

The equation for the dividends earned this year would be:

.10*x + .01*y = 826

You need to solve these two equations simultaneously to get your answer.

Solving them simultaneously means the same answer applies to both equations.

The two equations are:

.09*x + .03*y = 1047 (first equation)
.10*x + .01*y = 826 (second equation)

Leave the first equation alone and multiply the second equation by 3 to get

.09*x + .03*y = 1047 (first equation)
.30*x + .03*y = 2478 (second equation multiplied by 3)

Subtract the first equation from the second equation to get:

.21*x = 1431 (third equation)

divide both sides of the third equation by .21 to get:

x = 1431/.21 = 6814.285714

substitute for x in the first equation.

first equation equals:

.09*x + .03*y = 1047 (first equation)

substitute 6814.285714 for x to get:

.09*6814.285714 + .03*y = 1047

simplify to get:

613.2857143 + .03*y = 1047

subtract 613.2857143 from both sides of the equation to get:

.03*y = 1047 - 613.2857143 = 433.7142857

divide both sides of this equation by .03 to get:

y = 433.7142857/.03 = 14457.14286

Your answers are:

You invested 6,814.285714 in the first fund.

You invested 14,457.14286 in the second fund.

If you remember, x represented the money invested in the first fund and y represented the money invested in the second fund.

.09*x + .03*y = 1047 (last year dividends)

.10*x + .01*y = 826 (this year dividends)

the numbers check out so you can assume the answer is correct.

The information for last year plus the information for this year, solved simultaneously, allowed you to determine how much money was invested in each account.