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# Algebra

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Find the cost of a pencil and eraser if two pencils and three erasers cost 140 dollars, and fivepencils and four erasers cost 250 dollars.​

Sep 23, 2021

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Find the cost of a pencil and eraser if two pencils and three erasers cost 140 dollars, and fivepencils and four erasers cost 250 dollars.​

Let P stand for the cost of one pencil

Let E stand for the cost of one eraser

2P + 3E = 140  multiply both sides of the equation by 4 to get   8P + 12E = 560    (call this eq 3)

5P + 4E = 250  multiple both sides of the equation by 3 to get 15P + 12E = 750    (call this eq 4)

subtract eq 3 from eq 4 and you get  7P = 190

P = 190 / 7 = 27.14 dollars for one pencil

plug the value of P back into one of the original equations

(2 • 27.14) + 3E = 140

54.28 + 3E = 140

3E = 140 – 54.28 = 85.72

E = 85.72 / 3 = 28.57 dollars for one eraser

Those are some pretty expensive writing instruments.

Check answer.  Plug values into one of the original equations:

(5 • 27.14) + (4 • 28.57)

135.70 + 114.28                         =  249.98

The original problem specified 250 .... 249.98 is close enough, owing to rounding values

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Sep 23, 2021