How to Solve a Ticket Word Problem with a System

Problem

\text{10 tickets: adult } \$8, \text{ child } \$5, \text{ total } \$68

Answer

\text{6 adult, 4 child}

A ticket problem gives you two facts: how many items, and how much they cost together. Each fact becomes one equation.

Step-by-step solution

Name the unknowns and write the count equation.
$a + c = 10$
Why: The number of adult tickets plus the number of child tickets is 10.
Write the money equation.
$8a + 5c = 68$
Why: Each adult ticket adds 8 dollars and each child ticket adds 5 dollars to the total.
Substitute c = 10 - a from the count equation.
$8a + 5(10 - a) = 68$
Why: One equation with one variable can now be solved.
Solve for a.
$3a + 50 = 68 \Rightarrow 3a = 18 \Rightarrow a = 6$
Why: Combine like terms, then divide by 3.
Find c and answer the question.
$c = 10 - 6 = 4$
Why: The two values together must satisfy both equations.

Swapping the prices so the adult price multiplies c. Match each price to its own variable.
Writing only the money equation and forgetting that the ticket counts add to 10.
Using the total as a count instead of dollars. 10 tickets is not 68 dollars.

Use the same method. Work each problem on paper, then open the answer to check.

$\text{12 tickets: adult } \$9, \text{ child } \$6, \text{ total } \$96$

Show answer

$\text{8 adult, 4 child}$
$\text{8 tickets: adult } \$10, \text{ child } \$7, \text{ total } \$71$

Show answer

$\text{5 adult, 3 child}$
$\text{20 coins, nickels and dimes, total } \$1.40$

Show answer

$\text{12 nickels, 8 dimes}$
$\text{15 tickets: adult } \$7, \text{ child } \$4, \text{ total } \$81$

Show answer

$\text{7 adult, 8 child}$
$\text{10 tickets: adult } \$6, \text{ child } \$3, \text{ total } \$45$

Show answer

$\text{5 adult, 5 child}$