Question

a hotel has 243 rooms. those with kitchen facilities rent for 143 per night and those without kitchen facilities rent for 94 a night. on a night when the hotel was completely occupied, revenue was 27,105. how many of each room does the hotel have?

Answer 1

Let the hotel has x rooms with kitchen facilities and y rooms without kitchen facilities.

Then according to the given data, we have,

x + y = 243..............(1)

And, 143x + 94y = 27105............. (2)

.

Now, 143*(1) - (2) gives,

(143x + 143y) - (143x + 94y) = (143*243) - 27105

i.e. 143x + 143y - 143x - 94y = 34749 - 27105

i.e. 143y - 94y = 7644

i.e. 49y = 7644

i.e. y = 7644/49

i.e. y = 156

So from (1), x = 243 - 156 = 87

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So the hotel has 87 rooms with kitchen facilities and 156 rooms without kitchen facilities.