Question

At a concert, $1600 in tickets were sold. Adult tickets were $9 each and children’s tickets were $4 each. If the number of adult tickets was 30 fewer than twice the number of children’s tickets, how many of each kind were sold?

Name: Problem 474, Chapter 9: Prealgebra
Uploaded: 2023-11-14T04:02:58-08:00
Channel: Nick Johnson
Description: At a concert, 1600 in tickets were sold. Adult tickets were 9 each and children’s tickets were 4 each. If the number of adult tickets was 30 fewer than twice the number of children’s tickets, how many of each kind were sold?

   At a concert, $1600 in tickets were sold. Adult tickets were $9 each and children’s tickets were $4 each. If the number of adult tickets was 30 fewer than twice the number of children’s tickets, how many of each kind were sold?

Prealgebra

Lynn Marecek,… 1st Edition

Chapter 9, Problem 474

Instant Answer

Solved by Expert Nick Johnson

11/14/2023

Step 1

Let's denote the number of adult tickets as $a$ and the number of children's tickets as $c$. We know that the total money made from selling tickets is $1600, and the price of an adult ticket is $9 and a children's ticket is $4. So, our first equation is $9a + 4c = Show more…

Show all steps

Thanks for your feedback!

At a concert, $1600 in tickets were sold. Adult tickets were $9 each and children’s tickets were $4 each. If the number of adult tickets was 30 fewer than twice the number of children’s tickets, how many of each kind were sold?

Play audio

Feedback

Nick Johnson and 90 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

System of Linear Equations

This concept involves setting up and solving multiple equations that contain the same variables. In many real-world problems, such as determining the number of items sold with different prices, relationships between the quantities can be modeled using linear equations that are solved simultaneously.

Translation of Word Problems

The ability to convert a word problem into mathematical equations is crucial. This involves identifying the unknown quantities, assigning variables to them, and expressing the relationships and constraints described in the narrative as algebraic equations.

Substitution Method

A common technique for solving a system of equations where one equation is solved for one variable and then substituted into another equation. This reduces the problem to a single equation with one unknown, making it easier to find the solution.

Please give Ace some feedback