Ono large box and two small boxus weigh a lotal of 100 pounds.One large box and four small boxes weigh a Inlal of 140 pounds. The weight imit of a trailer is 1200 pounds. Write an inequality that represents the numbers of large,, and small, y, boxes that can be loaded in the trailer. ysquare leqslant x+square ... -60 -20 -10 113 : 10 - 20

## Step 1: Define Variables and Equations<br />### Let $x$ represent the weight of a large box and $y$ represent the weight of a small box. We can set up a system of equations based on the given information:<br />$x + 2y = 100$<br />$x + 4y = 140$<br /><br />## Step 2: Solve for $y$<br />### Subtract the first equation from the second equation to eliminate $x$:<br />$(x + 4y) - (x + 2y) = 140 - 100$<br />$2y = 40$<br />$y = 20$<br /><br />## Step 3: Solve for $x$<br />### Substitute the value of $y$ (20) back into the first equation:<br />$x + 2(20) = 100$<br />$x + 40 = 100$<br />$x = 60$<br /><br />## Step 4: Write the Inequality<br />### Let 'L' be the number of large boxes and 'S' be the number of small boxes. The total weight must be less than or equal to 1200 pounds. Since a large box weighs 60 pounds and a small box weighs 20 pounds, the inequality is:<br />$60L + 20S \le 1200$<br /><br />## Step 5: Simplify the Inequality<br />### Divide the inequality by 20:<br />$3L + S \le 60$<br /><br />## Step 6: Rewrite in terms of S<br />### Isolate S:<br />$S \le -3L + 60$