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tem of linear... medical study Piskel Fre A delivery truck is transporting boxes of two sizes: large and small. The combined weight of a large box and a small box is 55 pounds. The truck is transporting 55 large boxes and 70 small boxes. If the truck is carrying a total of 3250 pounds in boxes, how much does each type of box weigh?Large box: ? pounds Small box: ? pounds

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SOLUTION

From the question

The truck is transporting large boxes and small boxes

Let the weight of one large box be L

and let the weight of one small box be s

We are told that the combine weight of large box and small box is 55, that is

[tex]L+s=55.............equation1[/tex]

Also the truck is transporting 55 large boxes and 70 small boxes. And both totaling 3250 pounds

That is

[tex]55L+70s=3250[/tex]

Solving the equations simultaneously we have

[tex]\begin{gathered} L+s=55 \\ 55L+70s=3250 \\ Making\text{ L the subject in equation 1, we have } \\ L=55-s \end{gathered}[/tex]

Substituting the value of L for 55 - s into equation 2, we have

[tex]\begin{gathered} 55L+70s=3250 \\ 55(55-s)+70s=3250 \\ 3025-55s+70s=3250 \\ collecting\text{ like terms } \\ 15s=3250-3025 \\ 15s=225 \\ s=\frac{225}{15} \\ s=15 \end{gathered}[/tex]

Hence Small box weights 15 pounds

Substituting the value of 15 for s in equation 1, we have

[tex]\begin{gathered} L+s=55 \\ L+15=55 \\ L=55-15 \\ L=40 \end{gathered}[/tex]

Hence Large box weighs 40 pounds

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