A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 8 large boxes and 3 small boxes has a total weight of 1 delivery of 2 large boxes and 5 small boxes has a total weight of 57 kilograms. How much does each type of box weigh?

Explanation:

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