1. ## 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..?

2. Hello, -DQ-!

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.

3. Aww I get it! Stupid Me! the remaining one is the only one I ahven't gotten any thoughts?

4. Hello, -DQ-!

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