Question

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 2 large boxes and 6 small boxes has a total weight of 128 kilograms. A delivery of 5 large boxes and 3 small boxes has a total weight of 137 kilograms. How much does each type of box weigh?

Answer 1

Large box weighs 18.25 kilograms and small box weighs 15.25 kilograms.

Step-by-step explanation:

Let,

Large box = x

Small box = y

According to given statement;

2x+6y=128    Eqn 1

5x+3y=137     Eqn 2

Multiplying Eqn 2 by 2;

$2(5x+3y=137)\\10x+6y=274\ \ \ \ Eqn\ 3$

Subtracting Eqn 1 from Eqn 3

$(10x+6y)-(2x+6y)=274-128\\10x+6y-2x-6y= 146\\8x=146$

Dividing both sides by 8

$\frac{8x}{8}=\frac{146}{8}\\x=18.25$

Putting x=18.25 in Eqn 1

$2(18.25)+6y=128\\36.5+6y=128\\6y=128-36.5\\6y=91.5$

Dividing both sides by 6

$\frac{6y}{6}=\frac{91.5}{6}\\y=15.25$

Large box weighs 18.25 kilograms and small box weighs 15.25 kilograms.

Keywords: linear equations, subtraction

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