Practice: Writing and Solving Systems of Equations
1) A professional organizer charges a $45 consultation fee, plus $20 per hour. Her competitor charges a $30
consultation fee, plus $26 per hour.
a) Write a system of equations to represent the situation.
b) Solve the system by substitution. For what number of hours will the total charge be the same?
c) What will that charge be?
2) The sum of two numbers is -1. When twice the first number and four times the second number are added, the
sum is -10.
3) Briana’s family spent $134 on 2 adult tickets and 3 youth tickets at an amusement park. Max’s family spent
$146 on 3 adult tickets and 2 youth tickets. What is the price of a youth ticket?
4) At a bakery, Riley bought 3 bagels and 2 muffins for $7.25. Karen bought 5 bagels and 4 muffins for 13.25.
What is the cost of each item?
5) The length of a rectangle is 3 more than its width. The perimeter of the rectangle is 58 centimeters. What are
the rectangle’s dimensions?
6) Adam has dimes and quarters in his pocket. There are 28 coins in all, and they are worth $4.60 altogether.
How many quarters does Adam have?
Practice: Writing and Solving Systems of Equations
1) A professional organizer charges a $45 consultation fee, plus $20 per hour. Her competitor charges a $30
consultation fee, plus $26 per hour.
d) Write a system of equations to represent the situation.
e) Solve the system by substitution. For what number of hours will the total charge be the same?
f) What will that charge be?
2) The sum of two numbers is -1. When twice the first number and four times the second number are added, the
sum is -10.
3) Briana’s family spent $134 on 2 adult tickets and 3 youth tickets at an amusement park. Max’s family spent
$146 on 3 adult tickets and 2 youth tickets. What is the price of a youth ticket?
4) At a bakery, Riley bought 3 bagels and 2 muffins for $7.25. Karen bought 5 bagels and 4 muffins for 13.25.
What is the cost of each item?
5) The length of a rectangle is 3 more than its width. The perimeter of the rectangle is 58 centimeters. What are
the rectangle’s dimensions?
6) Adam has dimes and quarters in his pocket. There are 28 coins in all, and they are worth $4.60 altogether.
How many quarters does Adam have?