The charge for a single room at Hotel \(P\) is \(25\) percent less than the charge for a single room at Hotel \(R\) and

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The charge for a single room at Hotel \(P\) is \(25\) percent less than the charge for a single room at Hotel \(R\) and \(10\) percent less than the charge for a single room at Hotel \(G.\) The charge for a single room at Hotel \(R\) is what percent greater than the charge for a single room at Hotel \(G?\)

A. \(15\%\)
B. \(20\%\)
C. \(40\%\)
D. \(50\%\)
E.\(150\%\)

Answer: B

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Vincen wrote:
Wed Mar 31, 2021 7:33 am
The charge for a single room at Hotel \(P\) is \(25\) percent less than the charge for a single room at Hotel \(R\) and \(10\) percent less than the charge for a single room at Hotel \(G.\) The charge for a single room at Hotel \(R\) is what percent greater than the charge for a single room at Hotel \(G?\)

A. \(15\%\)
B. \(20\%\)
C. \(40\%\)
D. \(50\%\)
E.\(150\%\)

Answer: B

Solution:

We can let the charge for a room at hotel P = p, the charge for a room at hotel G = g, and the charge for a room at hotel R = r.

We are given that the charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. Thus:

p = 0.75r

And

p = 0.9g

Since both right-hand expressions are equal to p, we set them equal to each other, and then we solve for r.

0.75r = 0.9g

r = 1.2g

Thus, Hotel R’s rate is 20% greater than Hotel G’s rate.

Answer: B

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