A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 3 large boxes and 5 small boxes has a total weight of 112 kilograms. A delivery of 6 large boxes and 2 small boxes has a total weight of 118 kilograms. How much does each type of box weigh?

Let's call the weight of the large boxes:

l

Let's call the weight of the small boxes:

s

From the information in the equation we can now write two equations:

Equation 1:

5

l

+

3

s

=

99

Equation 2:

7

l

+

9

s

=

171

Step 1) Solve each equation for

9

s

:

Equation 1:

5

l

+

3

s

=

99

5

l

-

5

l

+

3

s

=

99

-

5

l

0

+

3

s

=

99

-

5

l

3

s

=

99

-

5

l

3

*

3

s

=

3

(

99

-

5

l

)

9

s

=

(

3

*

99

)

-

(

3

*

5

l

)

9

s

=

297

-

15

l

Equation 1:

7

l

+

9

s

=

171

7

l

-

7

l

+

9

s

=

171

-

7

l

0

+

9

s

=

171

-

7

l

9

s

=

171

-

7

l

Step 2) Because the left side of both equations are equivalent or the same we can equate the right side of each equation and solve for

l

:

297

-

15

l

=

171

-

7

l

297

-

171

-

15

l

+

15

l

=

171

-

171

-

7

l

+

15

l

126

-

0

=

0

+

(

-

7

+

15

)

l

126

=

8

l

126

8

=

8

l

8

15.75

=

8

l

8

15.75

=

l

l

=

15.75

Step 3) Substitute

15.75

for

l

in the solution to either equation in Step 1 and solve for

s

:

9

s

=

297

-

15

l

becomes:

9

s

=

297

-

(

15

*

15.75

)

9

s

=

297

-

236.25

9

s

=

60.75

9

s

9

=

60.75

9

9

s

9

=

6.75

s

=

6.75

The Solution Is:

The large boxes weigh 15.75 Kg

The small boxes weigh 6.75 Kg