Question

Hello I need help please :) and D. Says - The length of the stamp is 10 millimeters greater than the width

Answer 1

We are given the following system of equations:

$\begin{gathered} x=2y-10,(1) \\ 2x+2y=88,(2) \end{gathered}$

We can simplify equation (2) by dividing both sides by 2, we get:

$\begin{gathered} x=2y-10,(1) \\ x+y=44,(2) \end{gathered}$

Now, we substitute the value of "x" from equation (1) into equation (2):

$2y-10+y=44$

Now, we add like terms:

$3y-10=44$

Now, we add 10 to both sides:

$\begin{gathered} 3y-10+10=44+10 \\ 3y=54 \end{gathered}$

Now, we divide both sides by 3:

$y=\frac{54}{3}=18$

Now, we substitute this value of "y" in equation (1):

$\begin{gathered} x=2(18)-10 \\ x=36-10 \\ x=26 \end{gathered}$

Therefore, the length of the stamp is 26 mm and its width is 18mm.

We notice that:

$y=x-8$

This is due to the fact that:

$\begin{gathered} 18=26-8 \\ 18=18 \end{gathered}$

Therefore, the width of the stamp is 8mm less than the length.