GOZUNTA
Try it now
All courses Algebra I · A-CED.2 2 of 76
Create equations in two or more variables, graph them, and label axes/scales appropriately.

Write a two-variable equation using a constant rate

Problem
Each ticket costs \(\$12\). Write an equation relating the number of tickets \(t\) to the total cost \(C\).
Your answer
Show answer choicesHide answer choices Work through the mathematics first, then compare your reasoning.Select the answer that matches your work.
With a free account

Turn a few problems into a learning session.

Choose a course and objective, collect included problems into a session, and work through them in order.

Create a free account
With paid access

Build sessions from the full problem bank.

Choose the objective you need and make a learning session using all of its available problem types and variants.

Compare plans

Hint

Identify the constant rate, 12 dollars per ticket, and the variables t and C.

When there is no starting amount, the relationship is proportional: total = rate × number of items.

Solution walkthrough

01

Decode the variables

\[t~=~\text{number}~\text{of}~\text{tickets};~C~=~\text{total}~\text{cost}~\text{in}~\text{dollars}\]

The prompt assigns t to the ticket count and C to the resulting total cost. Thus t is the input and C is the output.

02

Identify the constant rate

\[\text{rate}~=~12~\text{dollars}/\text{ticket}\]

The phrase each ticket costs 12 dollars gives a rate of 12 dollars for every one ticket. There is no stated initial fee.

03

Use the proportional relationship

\[\text{total}~=~\text{rate}~\times~\text{count};~C~=~12t\]

A total with no starting amount equals the per-ticket rate multiplied by the number purchased. Substituting the stated rate gives C = 12t.

04

Check the units and a value

\[(12~\text{dollars}/\text{ticket})(2~\text{tickets})~=~24~\text{dollars};~C~=~12(2)~=~24\]

Ticket units cancel and leave dollars, as C requires. Two tickets would cost 24 dollars, confirming that the total grows by 12 dollars per ticket.

05

State the equation

\[C~=~12t\]

The equation relates the requested ticket count to total cost and exactly matches choice A.

+

Another way

  1. View the cost as repeated addition: t copies of 12 dollars sum to 12t dollars.

!

Common mistake

Do not write C = 12 + t. Twelve is a dollars-per-ticket rate, so it multiplies the number of tickets; it is not a fixed starting charge.

Solution walkthrough video