Answer:
1. 18x + 35y = 598
   x + y = 20 
   Isolate a variable in the second equation:
   y = -x + 20 
   Plug y back into the first equation
   18x + 35(-x + 20) = 598
   18x - 35x + 700 = 598 
   -17x +700 = 598 
   -17x = -102
    x = 6
    <u>You carpool 6 days of the 20</u>
    6 + y = 20
    y = 14
    <u>You ride the bus 14 days of the 20</u> 
2.   4.50n + 3p = 252
      p = 2n
      Substitute p into the first equation
      4.50n + 3(2n) = 252 
      4.50n + 6n = 252 
       10.5n = 252 
       n = 24
       <u>They sold 24 cans of nuts</u> 
       p = 2(24) 
       p = 48
       <u>They sold 48 boxes of popcorn</u>
       <u>The group sold, in total, 24 + 48 = 72 cans of nuts and boxes of popcorn. </u>
3.  x - y = 3 
     x + y = 8 
     Isolate a variable
     x = y + 3 
     (y + 3) + y = 8
     2y + 3 = 8 
     2y = 5 
     y = 2.5 
     <u>The average speed with wind is 2.5 mph</u> 
     x - 2.5 = 3 
     x = 5.5 
     <u>The average speed without wind is 5.5mph </u>
4. x + 8y = 22.8
    x + 6y = 18.6 
    Isolate
    x = -8y + 22.8
    Substitute
    (-8y + 22.8) + 6y = 18.6 
    -2y + 22.8 = 18.6
    -2y = -4.2
    y = -2.1
    <u>The gas costs $2.10 per gallon</u>
     x + 8(2.1) = 22.8 
     x + 16.8 = 22.8
     x = 6 
     <u>The cost of the car was is $6. </u>
5.  Cost = 9.99 + 2.49x
     Cost = 20.49 + 1.79x    
     To find which one is better, we need to set them equal to each other at first.
     9.99 + 2.49x = 20.49 + 1.79x 
     9.99 + 0.70x = 20.49
     0.70x = 10.5 
     x = 15
So, they cost the same at 15 rentals. 
To find which one is the better deal let's see how much both cost after 16 rentals. 
      Cost = 9.99 + 2.49(16) 
               = 49.83
      Cost = 20.49 + 1.79(16) 
               = 49.13
<u>Therefore, Main Street is the better deal because after the equilibrium Main Street costs less than Big Video. </u>
6.  x + y = 15
     .25x + .05y = 2.75 
     Isolate
     x = -y + 15 
     Solve
     .25(-y + 15) + .05y = 2.75 
     -.25y + 3.75 + .05y = 2.75
     -0.2y + 3.75 = 2.75
     -0.2y = -1
     y = 5 
     <u>There are 5 nickels</u> 
      x + 5 = 15 
      x = 10 
      <u>There are 10 quarters</u> 
7. x + y = 26 
    x + .25y = 17 
    Isolate 
    x = -y + 26 
    Substitute 
    (-y + 26) + .25y = 17
    -0.75y + 26 = 17
    -0.75y = -9 
    y = 12
    <u>There are 12 quarters in his pocket</u> 
    x + 12 = 26 
    x = 14 
    <u>There are 14 dollars </u>
<em>I hope this helps!!</em>
<em>- Kay :)</em>