Gloria, Teresa, and Rebecca went to an office supply store. Gloria bought 8 pencils, 4 markers, and 6 erasers. Her total was $22.00. Teresa spent $19.25 buying 5 pencils, 7 markers, and 8 erasers. Rebecca bought 5 pencils, 5 markers, and 4
erasers for $15.75. What is the cost of each item?

pencil: $2

marker: $0.75

eraser: $0.5

Step-by-step explanation:

Let the prices of one pencil, one marker, and one eraser be p, m, and e, respectively.

Gloria:

8p + 4m + 6e = 22         Eq. 1

Teresa:

5p + 7m + 8e = 19.25      Eq. 2

Rebecca:

5p + 5m + 4e = 15.75       Eq. 3

Subtract Eq. 3 from Eq. 2:

2m + 4e = 3.5                Eq. 4

Multiply Eq. 2 by 8 and subtract from it Eq. 1 multiplied by 5.

       40p + 56m + 64e = 154           Eq. 2 times 8

(-)     40p + 20m + 30e = 110            Eq. 1 times 5

                  36m + 34e = 44        

                  18m + 17e = 22              Eq.5

Now use Equations 4 and 5 as a system of two equations in two variables.

Multiply Eq. 4 by 18. Subtract Eq. 5 from it.

       36m + 72e = 63

(-)     36m + 34e = 44

                  38e = 19

e = 19/38

e = 0.5

Now substitute e = 0.5 into Eq. 4 to fond m.

2m + 4e = 3.5

2m + 4(0.5) = 3.5

2m + 2 = 3.5

2m = 1.5

m = 0.75

Substitute e = 0.5 and m = 0.75 into Eq. 1 to find p.

8p + 4m + 6e = 22

8p + 4(0.75) + 6(0.5) = 22

8p + 3 + 3 = 22

8p = 16

p = 2

pencil: $2

marker: $0.75

eraser: $0.5

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step-by-step explanation:

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