Respuesta :
For this, let
x : length of a postage stamp
y : width of a postage stamp
So you have the following system of linear equations
[tex]\mleft\{\begin{aligned}x=4\frac{3}{4}y \\ x+y+x+y=125\frac{1}{2}\end{aligned}\mright.[/tex]Because the perimeter is the sum of all the sides of a geometric figure. So, to solve the system of equations, we can first convert the mixed fractions to improper fractions, like this
[tex]\begin{gathered} 4\frac{3}{4}=\frac{4\cdot4+3}{4}=\frac{16+3}{4}=\frac{19}{4} \\ \text{ And} \\ 125\frac{1}{2}=\frac{125\cdot2+1}{2}=\frac{250+1}{2}=\frac{251}{2} \end{gathered}[/tex]Then,
[tex]\mleft\{\begin{aligned}x=\frac{19}{4}y \\ 2x+2y=\frac{251}{2}\end{aligned}\mright.[/tex]Now, you can replace the value of x from the first equation into the second and solve for y
[tex]\begin{gathered} \begin{aligned}2(\frac{19}{4}y)+2y=\frac{251}{2}\end{aligned} \\ \frac{38}{4}y+2y=\frac{251}{2} \\ \frac{38}{4}y+\frac{8}{4}y=\frac{251}{2} \\ \frac{46}{4}y=\frac{251}{2} \\ \text{ Multiply both sides of the equation by }\frac{4}{46} \\ \frac{4}{46}\cdot\frac{46}{4}y=\frac{251}{2}\cdot\frac{4}{46} \\ y=\frac{251}{23}=10\frac{21}{23}=10.91 \end{gathered}[/tex]Therefore, the width of the postage stamp is 251/23mm or 10 and 21/23mm.
the width of the postage stamp is 251/23mm or 10.91mm
