Carpenter A charges $50 an hour. Carpenter B charges $20 to visit your home plus $45 for each hour. For how many hours

carpenter-charges

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Carpenter A charges $50 an hour. Carpenter B charges $20 to visit your home plus $45 for each hour. For how many hours will the total cost for each carpenter be the same? How much will that cost be? If a customer thinks they need a carpenter for 3 hours, which carpenter should be hired?

Answer:

Carpenter A’s equation would be y=50x, x being the number of hours. Carpenter B’s equation would be y=45x+20. You can type these equations into your graphing calculator to get the intersecting point of these two lines (when both carpenters would charge the same amount). Strangely, my graphing calculator was acting up and an online calculator said no intersecting points, but when I did it I got 4 hours. I hope this helped somewhat

If y is cost and x is hour, carpenter A is y1=50x
and carpenter B is y2=45x+20.
The total cost for each carpenter will be the same when y1=y2 -> 50x=45x+20 -> 50x-45x=20 -> 5x=20 -> x=4. After 4 hours cost will be the same and it will be y1=504=200 (or y2=454+20=180+20=200)
If they need carpenter for 3hours cost will be y1=503=150 for A and y2=453+20=135+20=155 for B