Write and solve a system of equations that represents each situation. interpret the solution.
10. money neil has a total of twelve $5 and $10 bills in his wallet. he has 5 times as many $10 bills as $5 dollar bills. how many of each does he have?
11. hayride hillary and 23 of her friends went on a hayride. there are 8 more boys than girls on the ride. how many boys and girls were on the ride?
12. driving winston drove a total of 248 miles on monday. he drove 70 fewer miles in the morning than he did in the afternoon. how many miles did he drive in the afternoon?

10) There are 2 $5 bills and 10 $10 bills.
Given: number of bills = 12
             number of $5 = x
           number of $10 = 5x
  
x + 5x = 12
6x = 12
6x/6 = 12/6
x = 2  * number of $5 bills. ; no. of $10 = 5x = 5(2) = 10 bills.

11) Hillary and 23 friends = 24 total
      girls = x
      boys = x + 8

girls + boys = 24
x + x + 8 = 24
2x + 8 = 24
2x = 24-8
2x = 16
2x/2 = 16/2
x = 8 * number of girls ; no. of boys = x + 8 ⇒ 8 + 8 = 16

12) total no. of miles = 248
     miles drove in the morning = x - 70
     miles drove in the afternoon = x

x + x - 70 = 248
2x -70 = 248 
2x = 248 + 70
2x = 318
2x/2 = 318/2
x = 159 miles. *driven in the afternoon. 

driven in the afternoon : x - 70 = 159 - 70 = 89 miles driven in the morning