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2 years ago

Gloria, Teresa, and Rebecca went to an office supply store. Gloria bought 8 pencils, 4 markers, and 6 erasers. Her total was

Mathematics

1 answer:

emmainna [20.7K]2 years ago

8 0

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

----------------------------------------

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

Answer:

pencil: $2

marker: $0.75

eraser: $0.5

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