Question

I am not sure how to even start this problem or how to write it in equation form.

Answer 1

let x,y,z be the 3 installments.

You will get the equations:

x+y+z = 76000

.08x + .06y + .09z = 5940

The second last sentence states:

.08x = 6*(0.6y)

which is just:

x = 4.5y

Substitute into our two equations to get:

5.5y +z = 76000

.42y + .09z = 5940

The first equation, solve for z:

z = 76000 - 5.5y

Substitute that into the second equation:

.42y +6840 - 0.495y = 5940

-0.075y = -900

y = 12000

Now back substitute our y-value back into our original equation to get:

x = 54000

z = 10000

Since x is our first installment, the answer is $54000.

Answer 2

Answer: first part = $54,000, second part = $12,000, third part = $10,000

Explanation:

             Amount Invested        Rate              Interest

Part 1             x                            0.08              0.08x

Part 2            y                            0.06              0.06y

Part 3           z                           0.09             0.09z

TOTAL       76,000                     ******              5,940

• Since "the interest from the first investment is six times the interest from the second part",
• then 0.08x = 6(0.06y)
• ⇒      0.08x  = 0.36y
• ⇒               x = 4.5y

• Since x + y + z = 76,000
• then              z  = 76,000 - x - y
• ⇒                  z = 76,000 - 4.5y - y
• ⇒                  z = 76,000 - 5.5y

Interest:

0.08x + 0.06y + 0.09z = 5940

0.36y + 0.06y + 0.09(76,000 - 5.5y) = 5940

       0.42y       +        6840 - 0.495y   = 5940

                                  6840 - 0.075y   = 5940

                                            - 0.075y   = -900

                                              $\frac{-0.075}{-0.075}y$  = $\frac{-900}{-0.075}$

                                                       y   = 12,000

x = 4.5y  

x = 4.5(12,000)

x = 54,000

             Amount Invested        Rate              Interest

Part 1           54,000                  0.08              0.08(54,000) =  4,320

Part 2           12,000                   0.06              0.06(12,000) =     720

Part 3          10,000                   0.09             0.09(10,000) =     900  

TOTAL         76,000                  ******                                          5,940