Answer:
The woman invested $15,000 at 7% interest rate and $5,000 at 6% interest rate.
Step-by-step explanation:
We are given the following in the question:
Let x be the interest earned from 7% interest rate and y be the interest earned from 6% interest rate.
The woman invested has three times as much invested at 7% as she does at 6%.
Thus, we can write the equation:
![x = 3y](https://tex.z-dn.net/?f=x%20%3D%203y)
The total interest is $1,350.
Thus, we can write the equation:
![1350 = \dfrac{7x}{100} + \dfrac{6y}{100}\\\\7x + 6y = 135000](https://tex.z-dn.net/?f=1350%20%3D%20%5Cdfrac%7B7x%7D%7B100%7D%20%2B%20%5Cdfrac%7B6y%7D%7B100%7D%5C%5C%5C%5C7x%20%2B%206y%20%3D%20135000)
Solving the two equations by substitution method:
![7(3y) + 6y = 135000\\27y = 135000\\y = 5000\\x = 3(5000) = 15000](https://tex.z-dn.net/?f=7%283y%29%20%2B%206y%20%3D%20135000%5C%5C27y%20%3D%20135000%5C%5Cy%20%3D%205000%5C%5Cx%20%3D%203%285000%29%20%3D%2015000)
Thus, she invested $15,000 at 7% interest rate and $5,000 at 6% interest rate.