You can register a pickup truck as a passenger vehicle if the truck is not used for commercial purposes and the weight of the truck with its contents does not exceed 8500 pounds. Your pickup truck weighs 4200 pounds. Write an inequality to represent the numer of pounds your truck can carry and still qualify as a passenger vehicle. Then solve the inequality. A cubic yard of sand weighs about 1600 pounds. How many cubic yards of sand can you haul in your truck and still qualify as a passenger vehicle? Explain your reasoning.
Q#1:Your pickup truck weighs 4200 pounds. Write an inequality to represent the number of pounds your truck can carry and still qualify as a passenger vehicle. Then solve the inequality. A:Your truck can carry at most 4,300 pounds. Q#2:A cubic yard of sand weighs about 1600 pounds. How many cubic yards of sand can you haul in your truck and still qualify as a passenger vehicle? Explain your reasoning. A: You can haul at most 2.6875 cubic yards of sand.
2.6875
To represent the number of pounds your truck can carry and still qualify as a passenger vehicle, we can set up an inequality using the given information.
Let x represent the number of pounds of sand your truck can carry. Since the weight of your truck with its contents should not exceed 8500 pounds, the inequality would be:
4200 + x ≤ 8500
To solve the inequality, we need to isolate the variable x.
First, subtract 4200 from both sides of the inequality:
x ≤ 8500 - 4200
Simplifying further, we find:
x ≤ 4300
Now, we know that your truck can carry a maximum of 4300 pounds of sand and still qualify as a passenger vehicle.
To determine how many cubic yards of sand this corresponds to, we can use the given weight of 1600 pounds per cubic yard of sand.
Divide the maximum number of pounds your truck can carry (4300) by the weight of one cubic yard of sand (1600):
4300 ÷ 1600 ≈ 2.688
Therefore, you can haul approximately 2.688 cubic yards of sand in your truck and still qualify it as a passenger vehicle.