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

won't that be plagrisim thought?

step-by-step explanation:

sas (side angle side)

aa (angle angle)

sss(side side side)

sas find two sides with an angle in between

aa is finding two angles and the third will add up to 180

sss find all sides

step-by-step explanation: