Hotel rooms

In the 45 rooms, there were 169 guests. Some rooms were three-bedrooms and some five-bedrooms. How many rooms were there?

Correct answer:

a =  28
b =  17

Step-by-step explanation:


a+b = 45
3a + 5b = 169

a+b = 45
3·a + 5·b = 169

a+b = 45
3a+5b = 169

Pivot: Row 1 ↔ Row 2
3a+5b = 169
a+b = 45

Row 2 - 1/3 · Row 1 → Row 2
3a+5b = 169
-0.67b = -11.33


b = -11.33333333/-0.66666667 = 17
a = 169-5b/3 = 169-5 · 17/3 = 28

a = 28
b = 17

Our linear equations calculator calculates it.



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