Question

A truck that can carry no more than 6500lb is being used to transport refrigerators and upright pianos. Each refrigerator weighs 300lb and each piano weighs 475lb. Write and graph an inequality to show how many refrigerators and how many pianos the truck could carry. Will 10 refrigerators and 9 pianos overload the​ truck? Explain.

Answer 1

7275lb

Explanation:

Let R be the number of refrigerators and P be the number of pianos. The total weight of the load can be represented as:

Weight = 300R + 475P

The weight must be less than or equal to 6500lb, so we have the inequality:

300R + 475P <= 6500

To graph this inequality, we can first rewrite it in slope-intercept form:

475P <= 6500 - 300R

P <= (6500 - 300R) / 475

Next, we can plot the points (0, 13.68), (22, 0) on the coordinate plane, where (0, 13.68) corresponds to the y-intercept and (22, 0) corresponds to the x-intercept. The graph will be a line that starts at the y-intercept and goes down to the right, passing through (22, 0).

The truck could carry up to 22 refrigerators (when R = 22, P = 0), or up to 13.68 pianos (when R = 0, P = 13.68), or any combination of refrigerators and pianos that results in a weight of less than or equal to 6500lb.

As for the specific case of 10 refrigerators and 9 pianos, the weight can be calculated as:

Weight = 300 * 10 + 475 * 9 = 3000 + 4275 = 7275

This would overload the truck, as the weight of 7275lb is greater than the maximum allowed weight of 6500lb.

Answer 2

We can write an inequality to represent the weight that the truck can carry:

Weight of Refrigerators + Weight of Pianos <= 6500

Let x be the number of refrigerators and y be the number of pianos. Then we can write:

300x + 475y <= 6500

To determine if 10 refrigerators and 9 pianos would overload the truck, we can substitute the values into the inequality:

300 * 10 + 475 * 9 <= 6500

3000 + 4275 <= 6500

7275 <= 6500

Since 7275 is greater than 6500, this means that 10 refrigerators and 9 pianos would overload the truck.

Graphically, we can plot the points representing the weight of the refrigerators and pianos on the x-y plane, and shade the region below the line representing the inequality to show the combinations of refrigerators and pianos that would not overload the truck. Any point above the line would represent a combination of refrigerators and pianos that would overload the truck.

Hope it helps! : )