Question

Please answer this for me!!! 25 points to whoever answers this!!!!!!

Sean, Angelina, and Sharon went to an office supply store. Sean bought 7 pencils, 8 markers, and 7 erasers. His total was $22.00. Angelina spent $19.50 buying 4 pencils, 8 markers, and 6 erasers. Sharon bought 6 pencils, 4 markers, and 7 erasers for $17.75. What is the cost of each item?

Answer 1

Pencil = $0.25

Marker = $1.00

Eraser = $1.75

Explanation:

Let P denote pencils, M denote markers and E denote erasers. The quantities of each item and total amounts spent by each person can be modeled into the following linear system:

`7P+8M+7E=22\\4P+8M+6E=19.5\\6P+4M+7E=17.75`

Solving the linear system:

`7P-4P+8M-8M+7E-6E=22-19.5\\3P+E=2.5\\E=2.5-3P \\\\7P+8M+7E-2*(6P+4M+7E)=22-2*17.75\\-5P-7E=-13.5\\-5P*-7*(2.5-3P)=-13.5\\16P=-13.5+17.5\\P=0.25\\E=2.5-0.25*3\\E=1.75\\7P+8M+7E =22\\7*0.25+8M+7*1.75 =22\\8M=8\\M=1`

The price of each item is:

Pencil = $0.25

Marker = $1.00

Eraser = $1.75