Question

A fruit company delivers 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 95 kilograms. A delivery of 2 large boxes and 6 small boxes has a total weight of 68 kilograms. How much does each type of box weigh?

Answer 1

Each large box weighs 15.25 kg, and each small box weighs 6.25kg

Explanation:

Let's define the variables:

A = weight of a large box.

B = weight of a small box.

We know that:

"A delivery of 5 large boxes and 3 small boxes has a total weight of 95 kilograms."

We can write this as:

5*A + 3*B = 95 kg

We also know that:

"A delivery of 2 large boxes and 6 small boxes has a total weight of 68 kilograms."

2*A + 6*B = 68kg

Then we have the system of equations:

5*A + 3*B = 95 kg

2*A + 6*B = 68kg

To solve this, the first step is to isolate one of the variables in one of the equations.

I will isolate the variable A in the second equation:

A = 68kg/2 - 6*B/2 = 34kg - 3*B

A = 34kg - 3*B

Now we can replace this in the first equation:

5*( 34kg - 3*B) + 3*B = 95 kg

170kg - 15*B + 3*B = 95 kg

170kg - 12*B = 95 kg

170kg - 95kg = 12*B

75kg = 12*B

75kg/12 = B = 6.25kg.

Now we can replace this on the equation A = 34kg - 3*B to find the value of A.

A = 34kg -3*6.25kg = 15.25kg