A large box of fruit weighs 18.25 kilograms and a small box weighs 15.5 kilograms.
Step-by-step explanation:
Let,
Weight of large box = x
Weight of small box = y
According to given statement;
4x+8y=197 Eqn 1
2x+3y=83 Eqn 2
Multiplying Eqn 2 by 2
[tex]2(2x+3y=83)\\4x+6y=166\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 1
[tex](4x+8y)-(4x+6y)=197-166\\4x+8y-4x-6y=31\\2y=31[/tex]
Dividing both sides by 2
[tex]\frac{2y}{2}=\frac{31}{2}\\y=15.5[/tex]
Putting y=15.5 in Eqn 2
[tex]2x+3(15.5)=83\\2x+46.5=83 \\2x=83-46.5\\2x=36.5[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{36.5}{2}\\x=18.25[/tex]
A large box of fruit weighs 18.25 kilograms and a small box weighs 15.5 kilograms.
Keywords: linear equation, elimination method
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