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Carol is planning a trip to South Africa She plans to spend ten nights there, so she is investigating her options for lodging.
She has made arrangements to stay at least part of the time at a hostel, which is her cheapest option. However, she
would like to spend as many nights as she can in a private hotel. The hostel costs R 34 (34 rands) per night, and the
hotel costs R 55. If Carol has a budget of 430 rands for lodging, how many nights can she afford to stay in the private
hotel?
Six
b. five
C. four
d. three
a.
Please select the best answer from the choices provided

Respuesta :

sparklingsunset
The answer is four nights. If you do 55x4=220 and then the remaining days (6 left to calculate) 6x34=204 and 220+204=424. So I believe the answer is four nights. Hope this helps!

The number of nights that Carol can afford to stay in the considered private hotel is given by: Option C: four


How to interpret integral multiplication?

Suppose that there are two positive integer numbers( numbers like 1,2,3,.. ) as a and b

Then, their multiplication can be interpreted as:

[tex]a \times b = a + a + ... + a \: \text{(b times)}\\\\a \times b = b + b +... + b \: \text{(a times)}[/tex]

For example,

[tex]5 \times 2 = 10 = 2 + 2 + 2 + 2 + 2 \: \text{(Added 2 five times)}\\or\\5 \times 2 = 10 = 5 + 5 \: \text{(Added 5 two times)}[/tex]

Here, we're specified that:

  • Carol's budget (for stay, assumingly) = R 430
  • Hostel's cost = R 34 /night
  • Private hotel's cost = R 55/ night
  • She plans to spend: 10 nights
  • She has made plans to stay at least part of the time at the hostel.

So, assume that at max, she can spend 'n' nights in private hotel.

That the cost of these 'n' nights in hotel would be:

[tex]55 + 55 + \cdots + 55\: \: (\text{ n times }) = 55n[/tex]

This n is smaller than 10 as she is sure to spend some nights in hostel, and her trip is going to be of 10 days.

The number of nights she'd spend in hostel is 10 - n (so that n + (10-n) comes out as 10, the total number of night she wants to spend in her trip)

That the cost of these '10-n' nights in hostel would be:

[tex]34 + 34 + \cdots + 34\: \: (\text{ 10-n times }) = 34(10-n) = 340 - 34n[/tex]

Total cost she'd need to pay = cost of staying in hotel + cost of staying in hostel

= [tex]55n + 340 - 34n = (55-34)n + 340 = 21n + 340[/tex]

Now, this cost must be under her budget. That means, this cost should be either lower than the budget, or equal to it.

Thus, we get:
[tex]21n + 340 \leq 430\\\\\text{Subtracting 340 from both the sides}\\\\21n \leq 90\\\\\text{Dividing both the sides by 21}\\\\n \leq \dfrac{90}{21}\\\\n \leq 4.29...[/tex]

As 'n' is the maximum number of nights she can spend, and as number of nights she can spend is going to be in integer assumingly, and the greatest integer less than or equal to approx 4.29 number is 4

Thus, the number of nights that Carol can afford to stay in the considered private hotel is given by: Option C: four

Learn more about multiplication here:

https://brainly.com/question/26816519

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