Whitney invested $19,000, part at 5% and part at 7%. If the total interest at the end of the year is $1,110.,how much did she invest at 5%.
I know the answer is $11,000. I would like to know how to actually solve the equation.
let x = amount at 5%
19000-x = amount at 7%
Now, just add up the amount of interest, since they give you the total interest:
.05x + .07(19000-x) = 1110
.05x + 1330 - .07x = 1110
.02x = 220
x = 11000
So, 11000 at 5%
8000 at 7%
invested $1,110.00, how much was his rate of interest?
To figure out how much Whitney invested at 5%, we can set up a system of equations.
Let's denote the amount Whitney invested at 5% as x dollars. Since the total amount of money Whitney invested is $19,000, we can say that the amount she invested at 7% is (19,000 - x) dollars.
The next step is to set up equations for the interest earned on each investment. The interest earned on the amount invested at 5% can be calculated by multiplying the investment amount (x) by the interest rate (0.05):
Interest at 5% = 0.05 * x
Similarly, the interest earned on the amount invested at 7% can be calculated by multiplying the investment amount (19,000 - x) by the interest rate (0.07):
Interest at 7% = 0.07 * (19,000 - x)
Since the total interest at the end of the year is given as $1,110, we can write the equation:
Interest at 5% + Interest at 7% = $1,110
Substituting the previously calculated expressions for the interest earned:
0.05 * x + 0.07 * (19,000 - x) = $1,110
Simplifying this equation will allow us to solve for x, the amount invested at 5%.
0.05 * x + 0.07 * 19,000 - 0.07 * x = $1,110
0.05 * x + 1,330 - 0.07 * x = $1,110
-0.02 * x + 1,330 = $1,110
-0.02 * x = -$1,110 + $1,330
-0.02 * x = $220
Dividing both sides of the equation by -0.02, we get:
x = $220 / -0.02
x = -$11,000
Oops! It seems there was a sign mistake in the calculations. The answer should actually be $11,000, not -$11,000. Therefore, Whitney invested $11,000 at 5%.