An actor invests some money at 6%, and $44000 more than three times the amount at 11%. The total annual intere
earned from the investment is $36040. How much did he invest at each amount? Use the six-step method.
Step 1: Define the variables.
Let x be the amount invested at 6%.
Then 3x + 44000 is the amount invested at 11%.
Step 2: Write the equations.
The equation for the interest earned at 6% is 0.06x.
The equation for the interest earned at 11% is 0.11(3x + 44000).
Step 3: Combine the equations.
The combined equation is 0.06x + 0.11(3x + 44000) = 36040.
Step 4: Simplify and solve.
0.06x + 0.33x + 4840 = 36040
0.39x + 4840 = 36040
0.39x = 31200
x = 80000
Step 5: Substitute the value back into the original equations.
The amount invested at 6% is $80,000.
The amount invested at 11% is 3(80000) + 44000 = $224000.
Step 6: Check the answer.
0.06(80000) + 0.11(224000) = 36040
4800 + 24640 = 36040
36040 = 36040
The actor invested $80,000 at 6% and $224,000 at 11%.
Step 1: Assign variables.
Let x be the amount invested at 6%.
Let 3x+44000 be the amount invested at 11%.
Step 2: Set up equations.
The interest earned from the investment at 6% is 0.06x.
The interest earned from the investment at 11% is 0.11(3x+44000).
The total interest earned is $36040.
Step 3: Write the equation.
0.06x + 0.11(3x+44000) = 36040
Step 4: Simplify the equation.
0.06x + 0.33x + 4840 = 36040
0.39x + 4840 = 36040
Step 5: Solve for x.
0.39x = 36040 - 4840
0.39x = 31200
x = 31200 / 0.39
x ≈ 80000
Step 6: Calculate the other amount.
3x + 44000 = 3(80000) + 44000
3x + 44000 = 240000 + 44000
3x = 284000
x ≈ 94666.67
The actor invested approximately $80000 at 6% and approximately $94666.67 at 11%.
To solve this problem, we can use the six-step method:
Step 1: Assign Variables
Let's assign the variables:
x = amount invested at 6%
y = amount invested at 11%
Step 2: Translate the problem into equations
From the given information, we can create two equations:
Equation 1: The total investment is the sum of the investments at 6% and 11%:
x + y = Total Investment ----(Equation 1)
Equation 2: The total annual interest earned from the investment is $36040:
0.06x + 0.11y = $36040 ----(Equation 2)
Step 3: Simplify Equations (if needed)
Both equations are already simplified.
Step 4: Solve the equations
We can solve this system of equations using substitution or elimination method. Let's use the elimination method.
Multiply Equation 1 by 0.06 to match the coefficients of x in both equations:
0.06x + 0.06y = 0.06(Total Investment)
Now subtract this equation from Equation 2 to eliminate x:
0.06x + 0.11y - (0.06x + 0.06y) = $36040 - (0.06)(Total Investment)
0.05y = $36040 - 0.06(Total Investment)
Step 5: Solve for y
Simplify further:
0.05y = $36040 - 0.06(Total Investment)
0.05y = $36040 - 0.06(x + y) ----(Using Equation 1)
0.05y = $36040 - 0.06x - 0.06y
0.11y = $36040 - 0.06x
Step 6: Solve for x
Plug this expression for y in terms of x back into Equation 1:
x + y = Total Investment
x + ($36040 - 0.06x) = Total Investment
Now solve for x:
x + $36040 - 0.06x = Total Investment
0.94x = Total Investment - $36040
x = (Total Investment - $36040) / 0.94
Once you have the value of x, you can substitute it back into Equation 1 to find the value of y.