Question

one large box and two small boxes weigh a total of 160 pounds. one large box and four small boxes weigh a total of 160 pounds. the weight limit of a trailer is 600 pounds. write an inequality that represents the number 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 large box and a small box

Let the weight of a large box be \(x\) and the weight of a small box be \(y\).
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 \(y = 10\)
Substitute \(y = 10\) into \(x+2y=80\), we get \(x+2\times10=80\), \(x=60\)

Step2: Write the inequality

The weight limit of the trailer is \(600\) pounds. The total weight of \(x\) large boxes and \(y\) small boxes is \(60x+10y\).
The inequality is \(60x + 10y\leq600\)

Answer:

\(60x+10y\leq600\)