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 of ​$942 . This​ year, the first fund paid a​ 10% dividend and the second only​ 1%, and you received a total of ​$867 . How much money did you invest in each​ fund?

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 of ​$942 . This​ year, the first fund paid a​ 10% dividend and the second only​ 1%, and you received a total of ​$867 . How much money did you invest in each​ fund?

Question
Linear equations and graphs
asked 2020-12-05
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 of ​$942 . This​ year, the first fund paid a​ 10% dividend and the second only​ 1%, and you received a total of ​$867 . How much money did you invest in each​ fund?

Answers (1)

2020-12-06
Let x be the amount invested in the first fund and y be the amount invested in the second fund.
Last your, the interest was $858 so: 0.092x + 0.03y = 942 (1)
This year, the interest was $832 so:
0.10x + 0.01y = 867 2)
Solve by elimination. Here, I will eliminate y first. Multiply (2) by 3 to obtain (3): 0.30x + 0.03y = 2601 3)
Subtract each side of (1) and (3) and solve for x:
0.21x = —1659
\(\displaystyle{x}=—\frac{{1659}}{{-{0.21}}}\)
x=7900
Solve for y using (2): 0.10(7900) + 0.01y = 867
790+0.01y = 867
0.0ly = 77
y= 7700
So, the amounts invested are:
first fund \(\displaystyle—{>}\${7900}\)
second fund \(\displaystyle—\${7700}\)
0

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