Question

PLEASE HELP! 19 POINTS! NEED IT ASAP

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A truck that can carry no more than 6100 lb is being used to transport refrigerators and upright pianos. Each refrigerator weighs 300 lb and each piano weighs 475 lb. Write and graph an inequality to show how many refrigerators and how many pianos the truck could carry. Will 10 refrigerators and 8 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.
Graph the inequality.
Will 10 refrigerators and 8 pianos overload the​ truck? Explain.

Answer 1

Here, x represents the number of refrigerator in the truck and y represents the number of pianos in the truck.

As per the statement:

Each refrigerator weighs 300 lb and each piano weighs 475 lb.

then;

weight of the x refrigerator = 300x and

weight of the y piano = 475y

It is also given that:

A truck that can carry no more than 6100 lb is being used to transport refrigerators and upright pianos.

"no more than" means
`'\leq '`

then;

An inequality we get;

`300x+475y\leq 6100`

You can see the graph of the inequality as shown below.

From the graph we have:

Number of refrigerators (x) = 20 refrigerator

Number of pianos (y) = 13 pianos

Explain: Will 10 refrigerators and 8 pianos overload the​ truck.

x = 10 refrigerator

y = 8 pianos

Then substitute in the given inequality:

`300(10)+475(8)\leq 6100`

`3000+3800\leq 6100`

`6800\leq 6100` False.

The number of 10 refrigerator and 8 pianos will not overload the truck