Question

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?

Answer 1

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