a truck that can carry no more than 5600 lb being used to transport refrigerators and upright pianos. Each refrigerator weighs 300 lb and each piano weighs 525 lb. Write and graph an inequality to show how many refrigerators and how many pianos the truck could carry. Will 8 refrigerators and 6 pianos overload the truck? Explain.

Question

a truck that can carry no more than 5600 lb being used to transport refrigerators and upright pianos. Each refrigerator weighs 300 lb and each piano weighs 525 lb. Write and graph an inequality to show how many refrigerators and how many pianos the truck could carry. Will 8 refrigerators and 6 pianos overload the truck? Explain.

Answer 1

Let x be the number of refrigerators and y be the number of pianos.

Then, we have the following inequality:

300x + 525y ≤ 5600

This is because the total weight of the refrigerators and pianos cannot exceed the weight limit of the truck, which is 5600 lb.

To graph this inequality, we can first plot the line 300x + 525y = 5600. This line represents the maximum weight limit of the truck. Then, we shade in the region below the line, as this is where the total weight of the refrigerators and pianos is less than or equal to the weight limit of the truck.

To determine whether 8 refrigerators and 6 pianos will overload the truck, we plug in x = 8 and y = 6 into the inequality:

300(8) + 525(6) = 4800 + 3150 = 7950

Since 7950 is greater than the weight limit of the truck (5600 lb), 8 refrigerators and 6 pianos will overload the truck.

In general, we can solve for either x or y in the inequality and then plug in values to see if they satisfy the inequality.

Answer 2

Let x be the number of refrigerators in the truck and y be the number of pianos in the truck. Write an inequality to show how many refrigerators and how many pianos the truck could carry.

Answer 3

300x + 525y ≤ 5600

Answer 4

To write an inequality to show how many refrigerators and pianos the truck could carry, we can let 'r' represent the number of refrigerators and 'p' represent the number of pianos.

Given that the weight of each refrigerator is 300 lb and the weight of each piano is 525 lb, we can create the following inequality:

(300r) + (525p) ≤ 5600

Now, let's check if 8 refrigerators and 6 pianos will overload the truck.

Plugging in the values into the inequality:

(300 * 8) + (525 * 6) ≤ 5600

2400 + 3150 ≤ 5600

5550 ≤ 5600

Since 5550 is less than or equal to 5600, 8 refrigerators and 6 pianos will not overload the truck.