Question

robin can clean 72 rooms in 6 days how many can he clean in 9 days

Answer 1

Let's put it this way. 
It's a ratio of 6:72 and we need to change it in a way to find number of rooms cleaned in 9 days.

Divide 6 & 72 both by 2
Ratio is now 3:36

Multiply 3 & 36 both by 3
Ratio is now 9:108

The number of rooms in which Robin can clean in 9 days is 108 rooms. 

Answer 2

Hello!

Robin can clean 72 rooms in 6 days. How many rooms can Robin clean in 9 days?

We have a proportional magnitude (directly proportional), if we increase the number of days for cleaning, obviously we will have more rooms cleaned, then:

clean rooms __________ days

72 ----------------------------------- 6

y ------------------------------------- 9

$\dfrac{72}{y} = \dfrac{6}{9}$

multiply the means by the extremes

$6*y = 72*9$

$6\:y = 648$

$y = \dfrac{648}{6}$

$\boxed{\boxed{y = 108}}\Longleftarrow(clean\:rooms)\end{array}}\qquad\checkmark$

Answer:  

108 clean rooms in 9 days  

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I Hope this helps, greetings ... Dexteright02! =)