2014 AMC 12A Problem 2

Attempt Problem 2 of the 2014 AMC 12A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2014 AMC 12A solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

2.

At the theater children get in for half price. The price for 55 adult tickets and 44 child tickets is $24.50.\$24.50. How much would 88 adult tickets and 66 child tickets cost?
$35\$35
$38.50\$38.50
$40\$40
$42\$42
$42.50\$42.50
Answer: B
Concepts:ratio and proportion
Small hint:
A child ticket costs half an adult ticket, so measure everything in adult tickets
Big hint:
5+12⋅4=75+\tfrac12\cdot4=7 adult tickets cost $24.50\$24.50; find the cost of 8+12⋅6=118+\tfrac12\cdot6=11 adult tickets
Solution:
Since a child ticket is half an adult ticket, 55 adult and 44 child tickets equal 5+12⋅4=75+\tfrac12\cdot4=7 adult tickets, so one adult ticket costs 24.507=$3.50.\dfrac{24.50}{7}=\$3.50.
The second purchase equals 8+12⋅6=118+\tfrac12\cdot6=11 adult tickets, costing 11⋅3.50=$38.50.11\cdot 3.50=\$38.50.
Thus, the correct answer is B.
LIVE by Po-Shen Loh
Programs

LIVE Classes

Self-Paced Classes

Stars

Scholarship

About Us

Who Is Po-Shen Loh?

Email Contact

Newsletter

Jobs

Become a Star

For a more Thought Full world.

© 2026 Expii, Inc.