# Stressed!

• Feb 11th 2008, 03:09 PM
-DQ-
Stressed!
3) The number of positive intergers x with x < (or equal than, don't know how to do the line under it) such that each of the rational expressions

7x+1/2 , 7x+2/3 , 7x+3/4.......7x+300/301

^ The whole thing is over 2,3,4...301.. no just the closest number btw

is in lowest terms (i.e. in each expression, the numerator and demoninator have no common factors) is..?
• Feb 11th 2008, 05:05 PM
Soroban
Hello, -DQ-!

Quote:

2) In a pack of construction paper the number of blue and red sheets
are originally in the ratio 2:7.
Each day, a gril uses 1 blue and 3 red sheets.
One day she uses 3 red sheets and the last blue sheet.
At this time there are 15 red remaining.
How many sheets of paper were in the pack originally?

Let $\displaystyle 2n$ = number of blue sheets.
Let $\displaystyle 7n$ = number of red sheets.
. . Hence, the pack contains $\displaystyle 9n$ sheets.

During the next $\displaystyle d$ days, she takes $\displaystyle d$ blue and $\displaystyle 3d$ red sheets.

Then the number of remaining sheets are: .$\displaystyle \begin{Bmatrix}2n-d &\text{blue} \\7n-3d&\text{red}\end{Bmatrix}$

But we are told that the remaining sheets are: .$\displaystyle \begin{Bmatrix}0 &\text{blue} \\ 16 &\text{red}\end{Bmatrix}$

We have a system of equations: .$\displaystyle \begin{bmatrix}2n-d &=& 0 \\ 7n-3d &=&15\end{bmatrix}$

. . with the solution: .$\displaystyle n \,=\,15,\;d\,=\,30$

Therefore, there were: .$\displaystyle 9n\,=\,135$ sheets originally.

• Feb 11th 2008, 05:43 PM
-DQ-
Aww I get it! Stupid Me! the remaining one is the only one I ahven't gotten :D any thoughts?
• Feb 12th 2008, 02:47 PM
Soroban
Hello, -DQ-!

Don't delete your questions . . .

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