Question

Gloria, Tina, and Kelly went to an office supply store. Gloria bought 5 pencils, 7 markers, and 8 erasers. Her total was $19.00. Tina spent $21.00 buying 7 pencils, 5 markers, and 8 erasers. Kelly bought 4 pencils, 8 markers, and 7 erasers for $17.75. What is the cost of each item?

Answer 1

Answer:

Pencils cost $2

Markers cost $1

Erasers cost $0.25

Step-by-step explanation:

Let pencils be denoted by P, markers by M and erasers by E. The following linear system can be modeled from the data provided:

$5P+7M+8E = 19\\7P+5M+8E=21\\4P+8M+7E =17.75$

Solving the linear system:

$2P-2M= 2\\P=1+M\\4+4M+8M+7E =17.75\\\\12M+7E = 13.75\\12M+8E=14\\E=0.25\\M=\frac{14-0.25*8}{12}\\ M=1\\P=1+1=2$

Pencils cost $2

Markers cost $1

Erasers cost $0.25