Two investments totaling $64,500 produce an annual income of $3270. One investment yields 8% per year, while the other yields 2% per year. How much is invested at each rate?
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user, we need a system of equations.
x + y = 53500
.1x + .04y = 4030
(It doesn't matter which percent goes with x or y- we'd just get the answers reversed).
I'm also going to multiply the 2nd equation by 100 to get rid of the pesky decimals.
10x + 4y = 403000
Now, let's solve the first equation for x.
x = 53500 - y
Next, we substitute the right side for x in the 2nd equation
10(53500 - y) + 4y = 403000
535000 - 10y + 4y = 403000
-6y = -132000
y = 22000
x = 53500 - 22000 = 31500
Let's check.
10(31500) + 4(22000) = 403000
315000 + 88000 = 403000
403000 = 403000
Check!
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