Question

A truck that can carry no more than 6900 lb is being used to transport refrigerators and upright pianos. Each refrigerator weighs 200 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 16 refrigerators and 7 pianos overload the​ truck? Explain. 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 1

Part a) The inequality is
`200x+525y\leq 6,900`

The graph in the attached figure

Part b) 16 refrigerators and 7 pianos will not recharge the truck.

Explanation:

Part a) Write and graph an inequality to show how many refrigerators and how many pianos the truck could carry

Let

x -----> the number of refrigerators in the truck

y -----> the number of pianos in the truck

we know that

The number of refrigerators in the truck multiplied by 200 lb plus the number of pianos in the truck multiplied by 525 lb must be less than or equal to 6,900 lb

so

The inequality that represent this situation is

`200x+525y\leq 6,900`

using a graphing tool

The solution is the shaded area

Remember that the number of refrigerators or the number of pianos in the truck cannot be a negative number or a decimal number. The solution must be a whole numbers.

Part b) Will 16 refrigerators and 7 pianos overload the​ truck?

we know that

If a ordered pair is a solution of the inequality, then the ordered pair must satisfy the inequality

we have the ordered pair

(16,7)

Substitute x=16,y=7 in the inequality

`200(16)+525(7)\leq 6,900`

`3,200+3,675\leq 6,900`

`6,875\leq 6,900` -----> is true

The ordered pair satisfy the inequality

so

The ordered pair is a solution of the inequality

therefore

16 refrigerators and 7 pianos will not recharge the truck.