has inherited $15,000 that she wants to invest in two separate accounts, one paying 4%
and one paying 3% annual interest. If the total interest earned for a year is $550, how much
should she invest at each rate?
amount at 4% --- x
amount at 3% --- 15000 - x
solve for x ....
.04x + .03(15000-x) = 550
To determine how much money she should invest at each rate, we'll use the concept of weighted averages.
Let's represent the amount of money she invests at 4% interest by 'x' dollars. Since she wants to invest a total of $15,000, the amount she invests at 3% interest would be $15,000 - x.
Now, let's calculate the interest earned on each investment:
Interest earned at 4% = x * 0.04 = 0.04x
Interest earned at 3% = (15,000 - x) * 0.03 = 0.03(15,000 - x)
According to the problem, the total interest earned for a year is $550. So, we have the equation:
0.04x + 0.03(15,000 - x) = 550
Let's simplify the equation:
0.04x + 450 - 0.03x = 550
0.01x = 550 - 450
0.01x = 100
Divide both sides by 0.01:
x = 10,000
Therefore, she should invest $10,000 at 4% interest and $15,000 - $10,000 = $5,000 at 3% interest.