CPhill

36x + 9     is all we can do.....these are unlike terms, so we can't add them as such

This is a straight line......here's the graph.........https://www.desmos.com/calculator/0juzyo6k8e

If this is

(3/4) (1 + 1/3)  + (1 + 1/3)  =

(3/4)(4/3) + (1 + 1/3 ) =

1 +  (1 + 1/3)  =  

2 + 1/3 =

7/3

If this is 

(4/3) [ (1 + 1/3) + (1 + 1/3)] =

(4/3) [ 4/3 + 4/3 ] =

(4/3) [ 8/3]  =

32/9

99 factors as 9 x 11

117 factors as 9 x 13

Thus, we could use 9 trays, each holding  11 hot dogs and 13 buns

Guest...it would be difficult to solve this by using Algebra........we can use a Calculus technique, but it's a little difficult........

Here's a graphical solution :   https://www.desmos.com/calculator/xh6bf1qslg

The solution is that p = about 1.395

35/25  = 7/5

The faster rummer completes 1/4 of a lap in one minute when the slower runner completes 1/19  of a lap in one minute

So  

(1/4 - 1/19)T = 1

(15/76)T = 1    multiply both sides by  76/15

T = 76/15 min  = about 5.066 min

Proof

In 5.066min the faster runner runs  5.066(1/4)   = 1.266 laps

In 5.066min the slower runner runs 5.066(1/19)  = .266 laps

Thus....the first runner runs one more lap in 5.066 min

147 / (8 + 1/6)   = 

147 / (49/6)  =

(147) x (6/49)  =

147/49  x 6  =

3  x 6 =    18 mi/gal

Here's the graph :  https://www.desmos.com/calculator/jqfizeqyk7

Sorry....your question doesn't make any sense to me....did you leave something out????