Two investments totaling $38,500$38,500 produce an annual income of $2805$2805. One investment yields 3%3% per year, while the other yields 9%9% per year. How much is invested at each rate?
Question
Two investments totaling 38,500 produce an annual income of 2805. One investment yields 3%3% per year, while the other yields 9%9% per year. How much is invested at each rate?
Solution
Let's denote the amount invested at 3% as x and the amount invested at 9% as y.
From the problem, we have two equations:
-
x + y = 38,500)
-
0.03x + 0.09y = 2805, and each investment contributes its amount times its interest rate to the total income)
We can solve this system of equations step by step:
Step 1: Multiply the first equation by 0.03 to make the coefficients of x in both equations the same:
0.03x + 0.03y = $1155
Step 2: Subtract the new equation from the second equation:
0.06y = $1650
Step 3: Solve for y:
y = 27,500
Step 4: Substitute y = $27,500 into the first equation to solve for x:
x = 27,500 = $11,000
So, 27,500 is invested at 9%.
Similar Questions
Two investments totaling $18,000$18,000 produce an annual income of $1370$1370. One investment yields 7%7% per year, while the other yields 8%8% per year. How much is invested at each rate?
Last year Sarah invested money in two accounts. The first account had an interest rate of 4%4% and the second account had an interest rate of 3%3%. If she invested $700$700 more in the first account than the second and her total interest income was $392$392, how much did she invest at each rate?
Last year Sarah invested money in two accounts. The first account had an interest rate of 3%3% and the second account had an interest rate of 2%2%. If she invested $600$600 more in the first account than the second and her total interest income was $388$388, how much did she invest at each rate?Step 3 of 3: Solve the equation found in part 2 for x. Use this information to answer the given word problem.
he correct answerA, B and C invest Rs. 4000, 5000 and 6000 respectively in a business and A gets 25% of profit for managing the business, the rest of the profit is divided by A, B and C in proportion to their investment. If in a year, A gets Rs. 200 less than B & C together, what was the total profit for that year?
1. 500 was invested at 12% per annum simple interest and a certain sum of money invested at 10% per annum simple interest. If the sum of the interest on both the sum after 4 years is 480, the latter sum of money is ?450 750 600 550
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.