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April 13th, 2018, 08:40 AM   #1
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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?

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April 13th, 2018, 09:22 AM   #2
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After d days, we want: 45 + 4d = 36 + 4.45d
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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

$45+4d < 40 + 4.45d$
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April 13th, 2018, 12:55 PM   #4
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Quote:
Originally Posted by skeeter View Post
$45+4d < 36 + 4.45d$
corrected inequality ...
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