Question

one large box and two small boxes weigh a total of 80 pounds. one large box and four small boxes weigh a total of 100 pounds. the weight limit of a trailer is 900 pounds. write an inequality that represents the numbers of large, ( x ), and small, ( y ), boxes that can be loaded in the trailer. identify the graph of the inequality.

Explanation:

Step1: Find the weight of a small box

Let the weight of a large box be \(x\) pounds and the weight of a small box be \(y\) pounds.
We have the system of equations:
\(

$$\begin{cases}x + 2y=80\\x + 4y=100\end{cases}$$

\)
Subtract the first equation from the second equation:
\((x + 4y)-(x + 2y)=100 - 80\)
\(x+4y - x - 2y=20\)
\(2y=20\), so \(y = 10\)

Step2: Find the weight of a large box

Substitute \(y = 10\) into \(x+2y = 80\)
\(x+2\times10=80\)
\(x+20=80\)
\(x=60\)

Step3: Write the inequality

The total weight of \(x\) large boxes and \(y\) small boxes is \(60x+10y\)
Since the weight limit of the trailer is 900 pounds, the inequality is \(60x + 10y\leqslant900\)
Divide each term by 10: \(6x + y\leqslant90\)

Answer:

\(6x + y\leqslant90\)