Baten80 wrote:

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%

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

p = 3r/4

AND

p = 0.9g

p = 9g/10

We need to determine what percent greater the charge is for hotel R than for hotel G. Thus, we need to evaluate (r - g)/g x 100. However, we first need to get variables r and g in terms of p.

r = 4p/3

AND

g = 10p/9

Substitute 4p/3 for r and 10p/9 for g and we have:

(r - g)/g x 100

[(4p/3 - 10p/9)/(10p/9)] x 100

[(12p/9 - 10p/9)/(10p/9)] x 100

[(2p/9)/(10p/9)] x 100

2/10 x 100 = 20 percent

Alternate 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 = .75r

And

p = .9g

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

.75r = .9g

r = 1.2g

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

Answer: B

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