Graph an inequality to show how many refrigerators and how many pianos the truck could carry?

Question

A truck that can carry no more than 5800 pounds is being used to transport refrigerators and up right pianos. Each refrigerator weighs 200 pounds and each piano weighs 475 pounds. How many refrigerators and how many pianos can do truck carry. And will 13 refrigerators and seven pianos over load the truck

Answer 1

can carry no more than 5800 pounds:  Weight ≤ 5800

Weight:  200r + 475p   where r=# refrigerators, p = # pianos

 

200r + 475p ≤ 5800

 

The above equation gives the limits of what the truck can carry.

How many refrigerators or pianos depends on how many of the

other are present also.  We can find how many of JUST refrigerators

or JUST pianos from:   200r ≤ 5800   or   475p ≤ 5800

 

200r ≤ 5800

r ≤ 5800/200

r ≤ 29 r

maximum of 29 refrigerators with no pianos

 

475p ≤ 5800

p ≤ 5800/475

p ≤ 12.21

maximum of 12 pianos with no refrigerators

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If we have 13 refrigerators and 7 pianos:

 

200(13) + 475(7) ≤ 5800

2600 + 3325 ≤ 5800

5925 ≤ 5800

 

Since 5,925 pounds is more than the 5,800 pound maximum weight limit,

yes, 13 refrigerators and 7 pianos would overload the truck.