Question 593·Medium·Algebra

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The equation $4p + 0.5c = 60$ represents the total printing time, in minutes, needed to produce $p$ posters and $c$ postcards at a print shop. If the shop produces $6$ posters, how many postcards can it produce in the same amount of time?

A two-variable linear equation can describe two kinds of items sharing one fixed total. If you know the count of one kind, substitute it so only the other count is unknown, then solve with a Desmos regression. The time left over isn't the number of items; each item takes a certain amount of time.

Hints

Hint 1
The coefficient of $p$ gives minutes per poster, so $4p$ is the time for all the posters. Replace $p$ with the given poster count. Which letter is left to find?
Hint 2
Both terms in the equation measure printing time. The postcard count is $c$ , while $0.5c$ measures minutes spent on postcards. What value of $c$ makes the total match?

Step-by-step

Substitute, then solve in Desmos
Step 1
Replace the poster count
Here $4$ is a rate, meaning minutes per poster, so $4p$ is the time spent on posters. The shop makes $6$ posters, so replace $p$ with $6$ :
$4(6)+0.5c=60.$
Now $c$ , the number of postcards, is the only unknown.
Step 2
Find the postcard count
Type $4(6)+0.5c\sim60$ in Desmos. The $\sim$ tells the regression to find a value of $c$ that makes both sides match. Under PARAMETERS, Desmos shows $c=72$ . Since $c$ counts postcards, the shop can produce 72 postcards in the given time. Choice D.

Question 593·Medium·Algebra

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