12000 was invested in two funds. the first made 5% interest and the second made 8%. the total interest earned was $768. How much wasinvested in each account.
amount invested at 5% ----x
amount invested at 8% -- 12000-x)
solve for x ....
.05x + .08(12000-x) = 768
I would suggest multiplying each term by 100 to get rid of those decimals
Invesed:
$X @ 5%.
$(12,000-X) @ 8%..
$768 = Tot. Int. earned.
0.05X + 0.08(12000-X) = 768
0.05x + 960 - 0.08x = 768
-0.03x = 768 - 960 = -192
X = $6400 @ 5%.
12,000 - X = 12000 - 6400 = $5600 @ 8%.
To find out how much was invested in each account, let's assign variables to represent the amounts invested.
Let's say x represents the amount invested in the first fund, which earns 5% interest.
Therefore, the amount invested in the second fund, which earns 8% interest, would be 12,000 - x.
Now, we can calculate the interest earned from each investment. The interest earned from the first fund would be 0.05x, and the interest earned from the second fund would be 0.08(12,000 - x).
According to the problem, the total interest earned was $768, so we can set up the following equation:
0.05x + 0.08(12,000 - x) = 768
Let's solve this equation step by step:
0.05x + 0.08(12,000 - x) = 768
0.05x + 960 - 0.08x = 768
-0.03x + 960 = 768
-0.03x = 768 - 960
-0.03x = -192
To solve for x, we divide both sides of the equation by -0.03:
x = (-192) / (-0.03)
x = 6400
Therefore, $6,400 was invested in the first fund, which earns 5% interest. To find the amount invested in the second fund, we subtract x from the total investment:
12,000 - x = 12,000 - 6,400 = $5,600
Therefore, $6,400 was invested in the first fund, and $5,600 was invested in the second fund.