Question

A fruit company packages fruit into two types of boxes: large and small this morning the company made two deliveriez.The table below shows the number of boxes in each delivery and total weight (in kilograms)Let x be the weight of each large boxlet y be the weight of each small boxHow much does each type of box weigh?

Answer 1

We can make a system of equations with the information given:

Let x be the weight of each large box

Let y be the weight of each small box

Then,

(1) 6x+5y=115

(2) 2x+3y=47

Now, we are going to isolate one variable on one of the equations, and then substite on the other:

(2) 2x=47-3y

x=47/2-3/2y

Now, we are going to substitute (2) in (1)

$\begin{gathered} 6(\frac{47}{2}-\frac{3}{2}y)+5y=115 \\ 141-9y+5y=115 \\ 141-4y=115 \\ 141-115=4y \\ \frac{26}{4}=y \\ y=6.5 \end{gathered}$

Then, having the weight of each small box, we are going to substitute y=6.5 in (2)

$\begin{gathered} 2x+3(6.5)=47 \\ 2x+19.5=47 \\ 2x=47-19.5 \\ x=\frac{27.5}{2} \\ x=13.75 \end{gathered}$

Each large box weighs 13.75 kg and each small box weighs 6.5 kg.