Word Translations, Gmat study guide 4, Chapter 1, pg 24, #12

[bensonhua]

Martin buys a pencil and notebook for 80 cents. At the same store, glorida buys a notebook and eraser for $1.20, and Zach buys a pencil and eraser for 70 cents. How much would it cost to buy 3notebooks, 3 erasers, and three pencils?

I went about it like this

P+N =80 or N = 80-P
N+E= 120 or E = 120-N
P+E = 70 or P=70-E

so 3N+3P+3E = ?

3(80-P)+3(120-N)+3(70-E) =
240-3P +360-3N + 210-3E =
3P+3N+3E = 810

The answer is 405, which my answer doubles. I see how the book does it, but not sure why this substitution does not work.

Thanks

[sunny.jain]

Why dont u add all the 3 equations

2p + 2E + 2 N = 270

P + E+ n = 135

3(P+E+N) = 3*135 = 405

[bensonhua]

I did, thats the book answer. Thats why I am asking why the substitution method doesnt work

[nimish.tiwari]

I did, thats the book answer. Thats why I am asking why the substitution method doesnt work

You forgot to subract one set of (P+N+E). you have found values of P,N,E. What you now need is multiply EACH of the sides of these individual equations by 3 and ADD them together and solve for both sides:

3N + 3E + 3P = 3(80-P) + 3(120-N) + 3(70-E)
3(N+E+P) = 240 -3P+360-3N+210-3E
= 810 - 3(P+N+E)
Taking -3(P+N+E) on LHS, you get:
6(N+E+P) = 810
==> 3(N+E+P) = 810/2 = 405.

[Ben Ku]

bensonhua:

3(80-P)+3(120-N)+3(70-E) =
240-3P +360-3N + 210-3E =
3P+3N+3E = 810 <= This does not follow from step above

What you did was somehow set the EXPRESSION 240 - 3P + 360 - 3N + 210 - 3E to equal 0, which does not make any sense. To avoid similar errors, it's helpful to write the entire equation on every line,
3N+3P+3E = 3(80-P)+3(120-N)+3(70-E)
3N+3P+3E =240-3P +360-3N + 210-3E
6P+6N+6E = 810
3P + 3N + 3E = 405

Hope that helps.