Question

The length of a postage stamp is 4 and 3/4 mm longer than it's width. The perimeter of the stamp is 125 and 1/2 mm. what is the width of the postal stamp

Answer 1

For this, let

x : length of a postage stamp

y : width of a postage stamp

So you have the following system of linear equations

`\mleft\{\begin{aligned}x=4(3)/(4)y \\ x+y+x+y=125(1)/(2)\end{aligned}\mright.`

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

`\begin{gathered} 4(3)/(4)=(4\cdot4+3)/(4)=(16+3)/(4)=(19)/(4) \\ \text{ And} \\ 125(1)/(2)=(125\cdot2+1)/(2)=(250+1)/(2)=(251)/(2) \end{gathered}`

Then,

`\mleft\{\begin{aligned}x=(19)/(4)y \\ 2x+2y=(251)/(2)\end{aligned}\mright.`

Now, you can replace the value of x from the first equation into the second and solve for y

`\begin{gathered} \begin{aligned}2((19)/(4)y)+2y=(251)/(2)\end{aligned} \\ (38)/(4)y+2y=(251)/(2) \\ (38)/(4)y+(8)/(4)y=(251)/(2) \\ (46)/(4)y=(251)/(2) \\ \text{ Multiply both sides of the equation by }(4)/(46) \\ (4)/(46)\cdot(46)/(4)y=(251)/(2)\cdot(4)/(46) \\ y=(251)/(23)=10(21)/(23)=10.91 \end{gathered}`

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