cannot figure a way to do this problem:
An investment of $98,000 was made by a business club. The investment was split into three parts and lasted for one year. The first part of the investment earned 8% interest, the second 6%, and third 9%. The total interest from the investments was $7560. The interest from the first investment was 3 times the interest from the second. Find the amounts of the three parts of the investment.
so I let the three investment amounts be E, S, and N
E+S+N=98000
7500=E*.08+S*.06+N*.09
E*.08=3*S*.06
I don't know how to figure out answer past that
Since E = 2.25 S (from the last equation), you can eliminate E from the other two equations. Then solve two equations in two unknows (S and N).
Follow the advice that BobPursley gave to Samantha.
To solve this problem, you can represent the three investment amounts as variables. Let's say the first investment amount is E, the second is S, and the third is N.
Based on the given information, we can establish the following equations:
1. E + S + N = 98000 (Equation 1) - This equation represents the total amount of the investment.
2. E * 0.08 + S * 0.06 + N * 0.09 = 7560 (Equation 2) - This equation represents the total interest earned from the investments.
3. E * 0.08 = 3 * (S * 0.06) (Equation 3) - This equation states that the interest from the first investment is 3 times the interest from the second investment.
Now, let's solve these equations step-by-step:
1. Using Equation 3, we can rewrite it as E = 3 * (S * 0.06) / 0.08.
Simplifying this expression, we get E = 2.25S (Equation 4).
2. Substitute Equation 4 into Equation 1 to get:
2.25S + S + N = 98000.
3. Combine like terms in Equation 2:
0.08E + 0.06S + 0.09N = 7560.
4. Substitute Equation 4 into Equation 2 to get:
0.08(2.25S) + 0.06S + 0.09N = 7560.
5. Simplify Equation 5 to:
0.18S + 0.06S + 0.09N = 7560.
6. Combine like terms in Equation 5:
0.24S + 0.09N = 7560.
Multiply by 100 to remove decimals: 24S + 9N = 756,000 (Equation 6).
7. Substitute Equation 4 into Equation 1 to get:
2.25S + S + N = 98000.
8. Simplify Equation 7 to:
3.25S + N = 98000.
9. Rearrange Equation 9:
N = 98000 - 3.25S (Equation 8).
Now, we have two equations with two variables, S and N. We can substitute Equation 8 into Equation 6:
24S + 9(98000 - 3.25S) = 756,000.
Solve this equation to find the value of S. Once you find S, you can substitute it back into Equation 8 to find the value of N. Finally, substitute S and N into Equation 1 to find the value of E.
I recommend using a calculator or an algebraic solver to find the precise values of S, N, and E.