A delivery truck is transporting boxes of two size: the combined weight of a large box and a small box is 65 pounds. The truck is transporti

Question

A delivery truck is transporting boxes of two size: the combined weight of a large box and a small box is 65 pounds. The truck is transporting 60 large boxes and 55 small boxes if the truck is carrying a total of 3775 pounds in boxes, how much does each type of box weigh?

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Melanie 1 week 2021-09-14T22:45:32+00:00 1 Answer 0

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    2021-09-14T22:47:31+00:00

    pretty much about the same as before.

    a = weight of a large box

    b = weight of a small box.

    we know their combined weight is 65 lbs, thus a + b = 65.

    we also know that the truck has 60 large ones, and 55 small ones, thus 60*a is the total weight for the large ones and 55*b is the total weight for the small ones, and we know that is a total of 3775, 60a + 55b = 3775.

    \bf \begin{cases} a+b=65\\ \boxed{b}=65-a\\ \cline{1-1} 60a+55b=3775 \end{cases}\qquad \qquad \stackrel{\textit{substituting on the 2nd equation}}{60a+55\left( \boxed{65-a} \right)=3775} \\\\\\ 60a+3575-55a=3775\implies 5a+3575=3775\implies 5a=200 \\\\\\ a=\cfrac{200}{5}\implies \blacktriangleright a = 40 \blacktriangleleft \\\\\\ \stackrel{\textit{since we know that}}{b=65-a\implies }b=65-40\implies \blacktriangleright b=25\blacktriangleleft

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