Nicole invested her savings in two investment funds. The $8000 that she invested in Fund A returned a 6% profit. The amount that she invested in Fund B returned a 2% profit. How much did she invest in Fund B, if both funds together returned a 3% profit?
Question
Nicole invested her savings in two investment funds. The $8000 that she invested in Fund A returned a 6% profit. The amount that she invested in Fund B returned a 2% profit. How much did she invest in Fund B, if both funds together returned a 3% profit?
Solution
Let's denote the amount Nicole invested in Fund B as x.
From the problem, we know that the total profit from both investments is 3%. This can be expressed as the sum of the profits from Fund A and Fund B, divided by the total investment (8000 + x), equals 3%.
The profit from Fund A is 6% of 480.
The profit from Fund B is 2% of x, which is 0.02 * x.
So, the equation we can set up from the problem is:
(480 + 0.02x) / (8000 + x) = 0.03
Solving this equation for x will give us the amount Nicole invested in Fund B.
First, we can multiply both sides of the equation by (8000 + x) to get rid of the denominator on the left side:
480 + 0.02x = 0.03 * (8000 + x)
This simplifies to:
480 + 0.02x = 240 + 0.03x
Subtract 0.02x from both sides:
480 = 240 + 0.01x
Subtract 240 from both sides:
240 = 0.01x
Finally, divide both sides by 0.01 to solve for x:
x = 240 / 0.01 = $24,000
So, Nicole invested $24,000 in Fund B.
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