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.
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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