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All courses Math I · A-CED.2 2 of 59
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 dollars. Write a two-variable equation relating number of tickets t and total cost C.
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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

Identify the variables

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

The question tells you that t counts tickets and C represents the total cost.

02

Identify the rate

\[12~\text{dollars}~\text{per}~\text{ticket}\]

Each ticket adds 12 dollars to the total cost.

03

Write the equation

\[C~=~12t\]

Total cost equals 12 times the number of tickets, so the correct equation is C = 12t.

04

Check the relationship

\[t~=~2~\Rightarrow~C~=~24\]

If 2 tickets are bought, the equation gives 24 dollars, which matches 12 dollars per ticket.

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Another way

  1. You can also reason from repeated addition: 12 + 12 + cdots + 12 for t tickets is 12t.

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Common mistake

A common mistake is to add instead of multiply. There is no starting fee here, so the relationship is C = 12t, not C = 12 + t.