Question

A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 10 cubic feet and the volume of each large box is 22 cubic feet. A total of 21 boxes of paper were shipped with a combined volume of 342 cubic feet. Determine the number of small boxes shipped and the number of large boxes shipped.

Answer 1

10 small boxes and 11 large boxes were shipped.

Step-by-step explanation:

Given,

Total boxes shipped = 21

Total volume of shipped boxes = 342 cubic feet

Volume of each small box = 10 cubic feet

Volume of each large box = 22 cubic feet

Let,

Number of small boxes = x

Number of large boxes = y

According to given statement;

x+y=21     Eqn 1

10x+22y=342    Eqn 2

Multiplying Eqn 1 by 10

$10(x+y=21)\\10x+10y=210\ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 2

$(10x+22y)-(10x+10y)=342-210\\10x+22y-10x-10y=132\\12y=132$

Dividing both sides by 12

$\frac{12y}{12}=\frac{132}{12}\\y=11$

Putting y=11 in Eqn 1

$x+11=21\\x=21-11\\x=10$

10 small boxes and 11 large boxes were shipped.

Keywords: linear equation, subtraction

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