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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