Question

Kyle, Margot and Carlynn went to the local craft store to purchase supplies for making decorations for the upcoming dance at the high school. Kyle purchased three sheets of craft paper, four boxes of markers and five glue sticks. His bill, before taxes was $24.40. Margot spent $30.40 when she bought six sheets of craft paper, five boxes of markers and two glue sticks. Carlynn, purchases totaled $13.40 when he bought three sheets of craft paper, two boxes of markers and one glue stick. Determine the unit cost of each item. Let p represent the cost of a sheet of craft paper. Let m represent the cost of a box of markers. Let g represent the cost of a glue sticks. Upload the ordered triple that represents the solution to this problem. Your soluton should be in the order (p, m, g)

Answer 1

We can form a system of 3 linear equations from the given information. Let's denote p as the cost of a sheet of craft paper, m as the cost of a box of markers, and g as the cost of a glue stick.

The first equation is from Kyle's purchase:
3p + 4m + 5g = 24.40

The second equation is from Margot's purchase:
6p + 5m + 2g = 30.40

The third equation is from Carlynn's purchase:
3p + 2m + g = 13.40

To solve this system, we can use matrix representation and methods to solve it.

Our matrix representing coefficients of unknowns (p, m, g) in the equations is:
[[3, 4, 5],
[6, 5, 2],
[3, 2, 1]]

And our target matrix (the result of equations) is:
[24.40, 30.40, 13.40]

Using methods to solve linear systems of equations (for instance, Gaussian elimination, Cramer's rule, or matrix inversion), we find the solution to be:
p = 1.75, m = 3.60, and g = 0.95.

We see, that a single unit of craft paper (p) costs $1.75, a box of markers (m) costs $3.60, and a single glue stick (g) costs $0.95. Therefore, our solution in the format of an ordered triple (p, m, g) is (1.75, 3.60, 0.95).