Volume of each small box is 7 cubic feet and the volume of each large box is 13 cubic feet. There were twice as many large boxes shipped as small boxes shipped and the total volume of all boxes was 165 cubic feet. How many small boxes were shipped and how many large boxes were shipped?

5 small boxes and 10 large boxes were shipped.

Step-by-step explanation:

Let x represent the number of small boxes that were shipped.

Let y represent the number of large boxes that were shipped.

Volume of each small box is 7 cubic feet and the volume of each large box is 13 cubic feet. The total volume of all boxes shipped was 165 cubic feet. This means that

7x + 13y = 165 - - - - - - - - - - - - 1

There were twice as many large boxes shipped as small boxes shipped. This means that

y = 2x

Substituting y = 2x into equation 1, it becomes

7x + 13 × 2x = 165

7x + 26x = 165

33x = 165

x = 165/33

x = 5

y = 2x = 2 × 5

y = 10

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18