Answer:
the number of child plates and adults plates were served is 125 and 155 respectively 
Step-by-step explanation:
Let us assume the child plate be x
And, the adult plates be y
Now according to the question 
x + y = 280 .................(1)
2.60x + 9.50y = 1797.50 .............(2)
Now multiply by 2.60x in equation (1)
2.60x + 2.60y = 728
2.60x + 9.50y = 1797.50
-6.90y = -1069.50
y = 155
So, x = 280 - 155
= 125
hence, the number of child plates and adults plates were served is 125 and 155 respectively 
 
        
             
        
        
        
Let X = total students in musical
  
Then (1/3) X = number of seniors
  
   1 + 6 + 11 + (1/3)X = X
  
               18 + (1/3)X = X
  
                            18 = (2/3)X
  
                  (3/2)(18) = X
  
                           27 = X
  
27 students in musical of which one third are seniors,  
there are 9 seniors in musical
hope this helped!
 
        
             
        
        
        
He has 148 marbles and 56 shells. I think I have that right, well im positive.
        
                    
             
        
        
        
Answer:
To find the measure of angle OPQ, we have two equations...
y+5x-17=180 because angles OPN and OPQ are supplementary...
AND
x+17+2x-4+y=180 because the total degrees of a triangle must add up to 180.
The equations...
5x+y=197
3x+y=167
solce the system of equations...
x=15
y=122
Since we wanted to solve for y, 122 is the answer.
The measure of angle OPQ is 122.