Answer:
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
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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
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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
Answer:
pencil: $2
marker: $0.75
eraser: $0.5
