The number of rooms at Hotel G is 10 less than twice the number of rooms at Hotel H. If the total number of rooms at Hotel G and Hotel H is 425, what is the number of rooms at Hotel G?
Question
The number of rooms at Hotel G is 10 less than twice the number of rooms at Hotel H. If the total number of rooms at Hotel G and Hotel H is 425, what is the number of rooms at Hotel G?
Solution
Let's denote the number of rooms at Hotel H as H and the number of rooms at Hotel G as G.
From the problem, we know two things:
- G = 2H - 10 (since the number of rooms at Hotel G is 10 less than twice the number of rooms at Hotel H)
- G + H = 425 (since the total number of rooms at both hotels is 425)
We can substitute the first equation into the second to solve for H:
2H - 10 + H = 425 3H - 10 = 425 3H = 435 H = 435 / 3 H = 145
Then, we substitute H = 145 into the first equation to find G:
G = 2*145 - 10 G = 290 - 10 G = 280
So, Hotel G has 280 rooms.
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