Diego works in the shipping department of a toy factory that makes radio-controlled helicopters. Small helicopters weigh 3 pounds each, and are shipped in a container that weighs 15 pounds. Large ones, on the other hand, weigh 4 pounds apiece, and are shipped in a container that weighs 12 pounds. If these boxes can hold a certain number of helicopters each, all of the packed containers will have the same shipping weight. What would the total weight be? How many helicopters would fit in either container?

Total weight = 24 pounds

Number of helicopters = 3

Step-by-step explanation:

Small helicopters :

Weight = 3 pound

Weight of container = 15

Large helicopters:

Weight = 4

Weight of container = 12

3x + 15 = 4x + 12

3x - 4x = 12 - 15

-x = - 3

x = 3

Total weight of the container :

3(3) + 15

9 + 15 = 24 pounds

Hence, number of helicopters which will fit in either container is 3

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)