David and Denise share n pears in the ratio of 4:9. How many pears does Denise have in terms of n?

Question

How do you set up this equation?

Answer 1

Total number of pears: n
David has: x
Denise has: y
x+y = n
x/y = 4/9

From the last equation:

x = (4/9) y

Plug this into the first equation:

(4/9) y + y = n

(4/9) y + (9/9) y = n

13/9 y = n

y = (9/13) n

Answer 2

Out of each set of 13 pears

David gets 4 and Denise gets 9

 

Thus, Denise gets 9/13 of the pears or

 

9n/13