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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  

.

 Sep 23, 2021

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