0.08a + 0.06b + (116000 – a – b)0.09 = 9000 …..(1)

0.08a = 4*0.06b = 0.24b …..(2)

From (2), a = 3b ……..(3)

Substituting this in (1):

0.24b + 0.06b + (116000 – 4b)0.09 = 9000

116000*0.09 – 0.06b = 9000

0.06b = 10440 – 9000 = 1440

b = 1440 / 0.06 = 24000

From (3):

a = 3*24000 = 72000

The first part was $72000, the second $24000, and the third

116000 – 96000 = $20000.

total investment 116000

1st part earned 8% interest

2nd part earned 6% interest

3rd part earned 9% interest

total interest 9000

interest from 1st=4 times interest from 2nd

If you use x to represent the first part of the investment, y to represent the 2nd part and z to represent the third part you can start to develop your equations:

We know that x+y+z=116000 because the problem tells us that the total investment was 116000 and was split into three parts.

So now we can start to deal with the interest stuff:

I=PRT (interest=principal * rate * time) is the formula you want to keep in mind for figuring this out. Time is usually designated in years.

Remember the first part of the investment was x, so that is the principal and not the 116,000….We know that this earned 8% interest, so if we convert that to decimal form we have .08

So we have the principal and we have the rate and the time is just one year, so multiplying by one will just give us the same number anyway, so we don’t have to worry about it for this particular problem. Therefore, interest on part one is .08x

The same idea for parts 2 and 3 …. we will end up with .06y for part 2 and .09z for part 3. Now to make this into an equation, the problem tells us “the total interest from the investments was 9000”, therefore .08x+.06y+.09z=9000

Do you see how I got that??

For the third equation, we need to look at our final fact here which is “The interest from the first investment was four times the interest from the second.” So we know the interest from the first investment was .08x and that is equal to four times the interest from investment two. Therefore, .08x=4(.06y)

We have our three equations in three variables:

x+y+z=116000

.08x+.06y+.09z=9000

.08x=4(.06y)

It may make life a bit easier if we simplify some of these equations a bit before attempting to solve for x, y, and z:

x+y+z=116000 (good as it is)

8x+6y+9z=900000 (multiply through by 100 to get rid of decimals)

.08x=.24 (multiply out the right side)

8x=24 (multiply by 100 to clear decimals)

x=3 (that just made everything a WHOLE lot easier because we know the value of x now!!)

Are you OK to take it from here and solve the equations??