Word problems: The income from the 10% investment exceeds th

[jhawk555]

The income from the 10% investment exceeds the total from the other two investments by $600.

I know that "exceeds" means "subtract" and the "by" means "equal". I am confused as to the equation when it states the total of the other two investments.

Would I enter it as "0.06x + 0.08y - 0.10z = 600"?

 

[stapel]

It might help if you posted the entire exercise....

Note: The equation you have posted means "the difference between the sum of the first two investments and the third investment is six hundred dollars"; in other words, the income from the first two exceeds the ten-percent investment by six hundred. I'm pretty sure this is backwards of what the exercise gave you.

When you reply, please clarify what you are "entering", and into what you are entering it.

Thank you.

Eliz.

 

[jhawk555]

It might help if you posted the entire exercise....

Actually, I typed it as it appeared in the book. It is a systems problem with 3 separate equations. That was the last equation that I couldn't understand how to format. I didn't have too many math problems that use "exceeds" in the question. This is the first time I've had to do one and my math book didn't list how.

Thanks for your help.

 

[Mrspi]

Did you not think it might help for us to see the OTHER two parts of the problem, so that we could make sense of the question you posted (which, by itself, is pretty vague)?

Please post the complete question, along with the definitions of the variables (x, y and z) that you have used.

I could guess at what you mean, but I hate to do that.

 

[jhawk555]

Did you not think it might help for us to see the OTHER two parts of the problem...? Please post the complete question, along with the definitions of the variables (x, y and z) that you have used.

I could guess at what you mean, but I hate to do that.

I see your point. I was hoping to spare those who looked at it I guess. Here goes.

Bart has 3 investments totaling $110,000. These investments earn interest at 6%, 8%, and 10% respectively. Bart's total income from these investments is $9400. The income from the 10% investment exceeds the total from the other two investments by $600. Find out how much Bart has invested at 6%.

 

[Mrspi]

Bart has 3 investments totaling $110,000. These investments earn interest at 6%, 8%, and 10% respectively. Bart's total income from these investments is $9400. The income from the 10% investment exceeds the total from the other two investments by $600. Find out how much Bart has invested at 6%.

Well....that's a bit better. But, you still didn't tell us what each variable represents.

So, I'll tell you what I would do (your opinion may differ!):

Let x = amount invested at 6%
Let y = amount invested at 8%
Let z = amount invested at 10%

Total amount invested is $110,000
So,
x + y + z = 110000

Total income from all three investments is $9400.
So,
.06x + .08y + .1z = 9400

Income from 10% investment (z) exceeds the income from the other two investments (x and y) by $600.

This means that if you subtract the total of the interest earned on the 6% and 8% investments FROM the interest earned on the 10% investment, you should get 600.

.1z - (.06x + .08y) = 600

Now, you can take it from here.....

You've got three equations in three variables:

x + y + z = 110000
.06x + .08y + .1z = 9400
.1z - (0.06x + 0.08y) = 600

Solve by your favorite method.

 

[jhawk555]

I'll tell you what I would do (your opinion may differ!):....

That's the nudge I needed. Thanks a bunch. Sorry it took so long to spit it all out.

happy holidays