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April 13th, 2018, 08:40 AM  #1 
Member Joined: Apr 2018 From: On Earth Posts: 34 Thanks: 0  Algebra question, least number of days?
Roland wishes to hire a drill. From the supplier he usually uses, the total cost is a fixed cost of £45 plus an extra cost of £4.00 per day. A rival supplier offers him a fixed cost of £36 plus an extra cost of £4.45 per day. (ii) Let d be the least number of days for which it is cheaper for Roland to hire the drill from his usual supplier. Find d. Now, what is meant by "least number of days", does it mean the first day on which the usual supplier become cheaper? Thanks 
April 13th, 2018, 09:22 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,110 Thanks: 908 
After d days, we want: 45 + 4d = 36 + 4.45d

April 13th, 2018, 09:33 AM  #3 
Math Team Joined: Jul 2011 From: Texas Posts: 2,767 Thanks: 1422 
reference the attached graph ... red line is the cost from the usual supplier blue line is the cost from the new supplier note that the usual supplier is more expensive until about 20something days by "least", the problem wants to know the first integer number of days when usual supplier is cheaper ... i.e., what is the least value of $d$ such that $45+4d < 40 + 4.45d$ 
April 13th, 2018, 12:55 PM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 2,767 Thanks: 1422  

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algebra, days, number, question 
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