Page 401 - Algebra 1

Application: Play Tickets
A school play charged adults $8 and students $5 for tickets. There were
75 people who attended the play. The box office collected $444. How many adults and how many students attended the play? Use substitution to solve.
SOLUTION
First define the variables. Let x = number of adults. Let y = number of students.
Translate the situation into a system of equations.
Example
4
Hint
To determine how to define the variables, look at the question. The question will indicate what needs to be found; that is, what is unknown. Variables represent the unknown.
x + y = 75 8x + 5y = 444
Adults plus students equals the total number of people.
The total amount of money collected can be found by multiplying the cost of the ticket by the number of people buying that kind of ticket.
Now use substitution to solve the system.
y = -x + 75 8x + 5(-x + 75) = 444
8x - 5x + 375 = 444 3x + 375 = 444
3x = 69 x = 23
Solve the first equation for y. Substitute -x + 75 for y in the second
equation.
Distribute.
Combine like terms.
Subtract 375 from both sides. Divide both sides by 3.
Substitute x = 23 into the first equation. Subtract 23 from both sides.
23 + y = 75 y = 52
The solution is (23, 52). There were 23 adults and 52 students at the play.
Check
First Equation
x + y = 75 23 + 52 75
75=75 ✓
Second Equation
8x + 5y = 444 8(23) + 5(52) 444 184+260 444
444 = 444 ✓
Lesson Practice
386 Saxon Algebra 1
Solve each system of equations by substitution. Check your answer.
a. y=4x-3
(Ex 1)
y = 3x - 5
c. 4x+3y=2
(Ex 3)
2x + y = 6
b. x=3y-11
(Ex 2)
5x + 2y = -4
d. 4x+3y=19
(Ex 3)
7x - 6y = -23