A distribution company ships apples and oranges in boxes, Apples are shipped in boxes that weigh 35 pounds each. Oranges are shipped in boxes that weigh 55 pounds each. A shipment going to a market
weighs 5,000 pounds total and contains 100 boxes. How many boxes of apples are in this shipment?
We wish to set up equations for the number of boxes and the total weight of the boxes. If \(A\) and \(O\) represent the number of apples and oranges, we get:
Weight in pounds:
$$\underbrace{35A}_\text{35 pounds per box of Apple} + \underbrace{55O}_\text{55 pounds per box of orange} = \underbrace{5{,}000}_\text{total pounds of all boxes} $$
Boxes:
$$A + O = 100 $$
We can solve this problem using elimination. Multiplying both sides of the second equation by 55 in order to eliminate 55O,
$$ A + O = 100 $$
$$ 55A+55O=5{,}500 $$
Bringing down the weight equation and subtracting:
$$ \begin{array} { c c c c}
&55A & 55O & 5{,}500\\
-&35A & 55O & 5{,}000 \\ \hline
& 20A & 0 & 500
\end{array}
$$
Solving for \(A\):
$$20A=500$$
$$A=\boxed{25} $$