# Thread: Setting up and solving equations to find the price of books

1. ## Setting up and solving equations to find the price of books

Hey guys, I am a new poster around here and I really can use a hand here!

I am in high school and I just cant do this one problem even though I have tried for hours...

So here's the deal, its a problem with 4 books and I need to find the prices for each one.

the clues are

- all the books without the 1st one gives a total of 42$- all the books without the 2nd one gives a total of 40$
- all the books without the 3rd one gives a total of 38$and - all the books without the 4th one gives a total of 36$

2. What have you tried.

Name the prices.

A, B, C, and D perhaps.

B+C+D = 42
A+C+D = 40

etc...

Let's see what you get.

3. I didnt get no where...
All that I can conclude was

A + B + C + D = X

B + C + D = 42 and X - 42 = A
A + C + D = 40 and X - 40 = B
A + B + D = 38 and X - 38 = C
A + B + C = 36 and X - 36 = D

4. Why did you introduce 'X'? Get rid of that. It's cute, but it doesn't get you anywhere.

Have you the ability to solve a well-defined 4x4 system of equations? The coefficients certainly are not challenging.

Just for the record, X = 52, but the problem statement certainly does not ask for that.
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