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Bond [772]
3 years ago
6

Twenty states in a country have​ four-star hotels. Assume the country has 50 states.​ (a) What fraction of the states can claim

at least one​ four-star hotel?​ (b) How many states do not have a​ four-star hotel?​ (c) Write the fraction of states without a​ four-star hotel.
Mathematics
1 answer:
marissa [1.9K]3 years ago
8 0
1) 20/50, 4/10, 2/5 of the states can claim at least one four star hotel.
2) 30/50,6/10,3/5 of the states are without a four star hotel.

Please vote my answer brainliest. thanks!

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Answer:  4r + 5(20-r) \le 92

=======================================

Explanation:

r = number of red pens

4r = cost of buying r red pens

example: if r = 10, then 4r = 4*10 = 40 is the total cost of buying 10 red pens

If John buys r red pens, then he must buy 20-r black pens so that r and 20-r add to 20.

John buys 20-r black pens, and at $5 each, so it will cost 5(20-r) dollars for just the black pens alone.

In total, John spends 4r + 5(20-r) dollars for all the pens (red & black)

We want $92 be the most he spends. This is the ceiling or highest value possible.

Therefore,

4r + 5(20-r) \le 92

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

Extra info:

If you want to solve for r, then

4r + 5(20-r) \le 92

4r + 5(20)+5(-r) \le 92 distribute

4r + 100 - 5r \le 92  

100 - r \le 92

100-r+r \le 92+r add r to both sides

100 \le 92+r

100-92 \le 92+r-92 subtract 92 from both sides

8 \le r

r \ge 8

So John must buy at least 8 red pens. The most he can buy is 20 red pens since he wants 20 pens total.

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