Janet invested $23,000, part at 6% and part at 17%. If the total interest at the end of the year is $2,260, how much did she invest at 6%?
Let x be the amount invested at 6%
Then 23,000 - x is invested at 17%.
0.06 x + 0.17 (23,000 - x) = 2260.
That equation can be solved fo x
15,000
To solve the equation 0.06x + 0.17(23,000 - x) = 2,260 for x, follow these steps:
1. Distribute 0.17 to both terms inside the parentheses:
0.06x + 0.17 * 23,000 - 0.17x = 2,260
2. Simplify the equation:
0.06x + 3,910 - 0.17x = 2,260
3. Combine like terms by subtracting 0.06x from 0.17x:
-0.11x + 3,910 = 2,260
4. Subtract 3,910 from both sides of the equation:
-0.11x = 2,260 - 3,910
5. Simplify the equation further:
-0.11x = -1,650
6. Divide both sides of the equation by -0.11 to isolate x:
x = -1,650 / -0.11
7. Perform the division to find the value of x:
x ≈ 15,000
Therefore, Janet invested approximately $15,000 at a 6% interest rate.