A local church purchases gospel tracts in boxes of 100. The table list the cost, including shipping and handling, of previous orders.

Question

A local church purchases gospel tracts in boxes of 100. The table list the cost, including shipping and handling, of previous orders.

Boxes Cost

12 $80.75

9 $62

21 $137

1) Write a function rule, c(x) modeling the cost of ordering x boxes of tracts.

2) What is the cost of each box of tracts?

3) What is the shipping and handling fee?

Please use point slope formulas or slope intercept form for solving.

Answer 1

Let x be the number of boxes and y the shipping and handling cost.

12x + y = 80.75

9x + y = 62

21x + y = 137

Assuming the shipping and handling cost is the same for each order:

Put the three equations into matrix form:

[12 1 80.75]

[ 9 1 62.00]

[21 1 137.00]

Converting the matrix to Reduced Row Echelon Form (RREF):

[1 0 6.75]

[0 1 5.25]

[0 0 0 ]

Which means the price per box is $6.75 and shipping and handling is $5.25.

1) C(x) = 6.75x + 5.25.

2) $6.75

3) $5.25