Hi! I'm happy to help with this.
When you solve a word problem, the first thing you want to do is read it super carefully. This lets you figure out what, exactly, you are being asked. Then you can pick out the right "tool" (equation) to figure out the answer. From there, you plug in the values you know and solve, then check your answer.
Here, we are asked to figure out how much Martina invested in two investment funds. We are told three things:
1. The total profit Martina made, from both investment funds, was $1,520.00.
2. Fund A paid 2 percent per year and Fund B paid 8 percent per year.
3. Martina invested $4,000.00 less in Fund A than she did in Fund B.
With this information, we can write an equation.
First, though, we have to keep in mind that the profit (return) that Martina made on her investment is the amount the fund paid out on her principal (money invested).
We know those amounts are two percent and eight percent for the two funds. We will multiply those amounts by the principal invested in each fund. Be sure to convert percentages to decimals.
Second, we have to focus on the fact that the amount Martina invested in A (the principal) is $4,000 less than what she invested in B. Therefore, A = B - 4,000.
Finally, whatever equation we write is going to equal $1,520 because that is the profit she made. So the interest rate multiplied by the principal of fund A plus the interest rate multiplied by the principal of fund B equals $1,520.
Here's the equation:
0.02A + 0.08B = 1,520
0.02(B-4000) + 0.08(B) = 1,520
Now let's solve:
0.02B - 80 + 0.08B = 1,520
.10B - 80 = 1,520
.10B = 1,600
B = $16,000
So we know now that Martina invested $16,000 in fund B.
Since the amount Martina invested in fund A is $4,000 less than that, she must have invested $12,000 in fund A.
Let's see if we are correct:
0.02($12,000) + 0.08($16,000) = 1,520
$240 + $1,280 = $1,520
We are correct!
