Question

A delivery truck is transporting boxes of 2 sizes large and small. the large box weighs 55lbs each and thr small boxes weigh 20lns each. there are 135 boxes in all. If the truck is carrying a total of 4975 in boxes how many of each biz is it carrying?

Answer 1

we can raise two equations with the statements

"there are 135 boxes in all", so large and small boxes sum 135

`\begin{gathered} x+y=135 \\ \end{gathered}`

where x are large and y small

"If the truck is carrying a total of 4975 lbs", so the total weight is 4975

`55x+20y=4975`

solve x from the first equation and replace on the second to find y

`\begin{gathered} x+y=135 \\ x=135-y \end{gathered}`

replacing:

`\begin{gathered} 55x+20y=4975 \\ 55(135-y)+20y=4975 \\ 7425-55y+20y=4975 \\ -55y+20y=4975-7425 \\ -35y=-2450 \\ y=(-2450)/(-35) \\ y=70 \end{gathered}`

so there are 70 small boxes, now replace y=70 on any equation to find x

`\begin{gathered} x+y=135 \\ x+(70)=135 \\ x=65 \end{gathered}`

and there are 65 large boxes