In actor inveseted in some money at 8% and 27,000.00 more than 3 times the amount of 12%, The annual interest is $56480. How much did he invest at each amount? Use the six-step
He invested $ _ at 8% and $_ at 12%
invested at 8% ----x
invested at 12% --- 3x+27000
.08x + .12(3x+27000) = 56480
times 100
8x + 12(3x+27000) = 5648000
continue following the "six-step" process that you learned
I do not know how to follow the six step. I have try and got confuse. Please solve it for me.
To solve this problem, you can follow the Six-step method:
Step 1: Assign variables to the unknowns.
Let's call the amount invested at 8% as x, and the amount invested at 12% as y.
Step 2: Write down the known information.
The invested amount at 8% is $27,000 + 3y.
The interest earned at 8% is 8% of x.
The interest earned at 12% is 12% of y.
The total annual interest earned is $56,480.
Step 3: Write down the equations.
The equation for the invested amount at 8% is x = 27,000 + 3y.
The equation for the interest earned is 0.08x + 0.12y = 56,480.
Step 4: Solve the equations simultaneously.
Substitute the value of x from the first equation into the second equation:
0.08(27,000 + 3y) + 0.12y = 56,480
2,160 + 0.24y + 0.12y = 56,480
0.36y = 56,480 - 2,160
0.36y = 54,320
Divide both sides by 0.36:
y = 54,320 / 0.36
y = 150,888.89 (rounded to two decimal places)
Substitute the value of y back into the first equation to find x:
x = 27,000 + 3(150,888.89)
x = 27,000 + 452,666.67
x = 479,666.67 (rounded to two decimal places)
Step 5: Check the solution.
Plug the values of x and y back into the original equations to ensure they satisfy both equations.
The invested amount at 8% is 27,000 + 3(150,888.89) = 27,000 + 452,666.67 = 479,666.67
The interest earned is 0.08(479,666.67) + 0.12(150,888.89) = 56,480.
Step 6: State the solution.
The actor invested $479,666.67 at 8% and $150,888.89 at 12%.