My Math Forum Algebra question, least number of days?

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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: 14,310 Thanks: 1023 After d days, we want: 45 + 4d = 36 + 4.45d Thanks from Country Boy and Student2018
April 13th, 2018, 09:33 AM   #3
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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 20-something 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

$45+4d < 40 + 4.45d$
Attached Images
 cost_problem.jpg (22.9 KB, 1 views)

April 13th, 2018, 12:55 PM   #4
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From: Texas

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Quote:
 Originally Posted by skeeter $45+4d < 36 + 4.45d$
corrected inequality ...

 Tags algebra, days, number, question

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