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ehidna [41]
3 years ago
7

Catie is starting a babysitting business. She spends $26 on flyers for advertising. She has an initial fee of $5 and then $3 per

hour. How many hours will she have to work to make a profit?
Mathematics
2 answers:
Olin [163]3 years ago
6 0
26+5= 31 correct?
So lets make a chart(ish lol)

Hours         $$$
1                     3
2                     6
3                     9
4                    12
5                      15 
6                      18
7                      21
8                      24
9                      27 
10                     30
11                       33
To get atleast 31 dollars you need to work 11 hours.
If you want fractions they need to work 10 1/3 hours
Hope this helped!

saveliy_v [14]3 years ago
3 0
Hi <span>Citytennisace . I have a different answer than </span>Zachary101234. 

In this question, you're working to find the total profit Catie will make minus any expenses incurred. In this case advertising. To put it another way: 

Total profit =  Revenue - Exp. 

Let us say profit is X. Rev is $5+$3 and Exp is $26 

5 + 3X = 26
--             --
5             5
      3X = 21
      --    --
       3     3
         X = 7

The above is explained in detail below: 

Now she only charges $5 for the first hour so: 

Hour 1: $5+$3 = 8 

She then charges $3 for each extra hour. To make things simple, you can subtract the cost for the initial hour from the adv. exp ($26-$5=$21) then divide the total by 3 ($21/3=7). This means that to break even, Catie has to work 7 hours. To make a profit, she must work 8.  
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======================================================

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-------------------

Explanation:

In the second step, I multiplied top and bottom by 1/x. This divides every term by x. Doing this leaves us with various inner fractions that have the variable in the denominator. Those inner fractions approach 0 as x approaches infinity.

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In a sense, the leading terms of the numerator and denominator are -2x and x respectively. They are the largest terms for each, so to speak. As x gets larger, the influence that -2x and x have will greatly diminish the influence of the other terms.

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I recommend making a table of values to see what's going on. Or you can graph the given function to see that it slowly approaches y = -2. Keep in mind that it won't actually reach y = -2 itself.

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