Question 602·Easy·Algebra

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A copy shop’s printer works at a constant rate of $12$ pages per minute. Which function $p$ models the number of pages the printer produces in $t$ minutes?

A constant rate in pages per minute tells you the same number of pages is made each minute. To write a function for any number of minutes, multiply the rate by the time so the minutes cancel. Dividing by the rate would help you find time from a known page count, not pages from a known time.

Hints

Hint 1
A unit rate tells you how many pages are made in one minute. Because that amount stays the same, what operation gives the total pages made in $t$ minutes?
Hint 2
The output $p(t)$ must count pages, not minutes. Multiply pages per minute by minutes, then check which units remain.

Step-by-step

Multiply rate by time
Step 1
Turn the rate into a page-count expression
No Desmos needed. The rate and its units give the relationship directly. A unit rate is an amount for one unit of time. The printer makes $12$ pages in each minute, so multiply pages per minute by minutes:
$p(t)=\left(12\frac{\text{pages}}{\text{minute}}\right)(t\text{ minutes}).$
Step 2
Cancel the time units
Cancel the minutes to get the number of pages:
$p(t)=12t.$
At $t=0$ , the printer has produced $0$ pages, so there's no starting amount to add. The printer produces $12t$ pages in $t$ minutes. Choice C.

Question 602·Easy·Algebra

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Step-by-step

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Strategy

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