Question

a fruit company delever its fruit in two types of boxes: large and small. A delivery of 5 large boxes and 3 small boxes has a total weight of 120 kilograms. A delivery of 7 large boxes and 9 small boxes has a total weight of 234 kilograms. how much does each type of bow weigh?

Answer 1

Let the weight of a large box be x .

Let the weight of a small box be y .

According to the first condition,

`5x\text{ + 3y = 120 \_\_\_\_\_\_\_(1)}`

According to the second condition,

`7x\text{ }+\text{ 9y = 234\_\_\_\_\_\_\_(2)}`

Multiplying equation ( 1 ) by 3 ,

`15x\text{ + 9y =360 \_\_\_\_\_\_(3)}`

Subtracting equation (2) from (3),

`\begin{gathered} 8x\text{ = 126} \\ x\text{ = }(126)/(8) \\ x\text{ = 15.75} \end{gathered}`

Substituting the value of x = 15.75 in equation ( 1 ),

`\begin{gathered} 5(15.75)\text{ + 3y = 120} \\ 78.75\text{ + 3y = 120} \\ 3y\text{ = 120 - 78.75} \end{gathered}`

Further,

`\begin{gathered} 3y\text{ = 41.25} \\ y\text{ = }(41.25)/(3) \\ y\text{ = 13.75} \end{gathered}`

Thus the weight of a larger box is 15.75 kilograms and weight of a smalller box is 13.75 kilograms.