The Solution:
Let the weight of a large box be x.
And the weight of a small box be y.
Given:
Delivery of 6 large boxes and 5 small boxes has a total weight of 180 kilograms.
[tex]6x+5y=180...eqn(1)[/tex]Delivery of 2 large boxes and 3 small boxes has a total weight of 78 kilograms.
[tex]2x+3y=78...eqn(2)[/tex]Solve the system of equations by the elimination method of simultaneous equations.
Step 1:
Multiply through eqn(2) by 3 to make the coefficients of x in both equations equal.
[tex]\begin{gathered} 3(2x+3y=78)=6x+9y=234 \\ 6x+9y=234...eqn(3) \end{gathered}[/tex]Step 2:
To eliminate the term in x, we shall subtract eqn(1) from eqn(3).
[tex]\begin{gathered} 6x+9y=234...eqn(3) \\ -(6x+5y=180)...eqn(1) \\ -------------- \\ 4y=54_ \\ \\ Divide\text{ both sides by 4, we get} \\ y=\frac{54}{4}=13.5\text{ kilograms} \end{gathered}[/tex]Step 3:
Substitute 13.5 for y in eqn(2) to get x.
[tex]\begin{gathered} 2x+3(13.5)=78 \\ 2x=78-40.5 \\ 2x=37.5 \end{gathered}[/tex]Dividing both sides by 2, we get
[tex]x=\frac{37.5}{2}=18.75\text{ kilograms}[/tex]Therefore, the correct answers are:
The weight of each large box = 18.75 kilograms
The weight of each small box = 13.5 kilograms
