Question 423·Easy·Algebra

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At a café, the total cost $C$ (in dollars) of buying $m$ muffins and $n$ drinks is given by the equation

C = 4m + 3n

If Sam spent $50 and bought $8$ muffins, how many drinks did he buy?

Your answer

A two-variable cost equation adds the costs of two kinds of items. If you know the total and one item count, substitute them into the equation and use a Desmos regression to find the other count. Each coefficient is a price per item, so the dollars spent on the remaining items aren't their count.

Hints

Hint 1
A coefficient is the number multiplying a letter. The terms $4m$ and $3n$ are dollar amounts. Which given values replace the total $C$ and the muffin count $m$ ?
Hint 2
After substitution, $n$ is the only unknown. A Desmos regression uses $\sim$ in place of $=$ to find the value that makes both sides match. Make sure you report a number of drinks, not a dollar amount.

Step-by-step

Substitute, then solve in Desmos
Step 1
Turn Sam's purchase into an equation
The coefficient $4$ is the price of one muffin, and $3$ is the price of one drink. So $4m$ and $3n$ are costs. Sam spent $50 and bought $8$ muffins, so replace $C$ with $50$ and $m$ with $8$ :
$50=4(8)+3n$
The $3n$ term measures dollars, not drinks.
Step 2
Find the number of drinks
Type $50\sim4(8)+3n$ in Desmos. The regression uses $\sim$ instead of $=$ to find the value of $n$ that makes the costs add to $50$ . Desmos shows $n=6$ under PARAMETERS. Since $n$ counts drinks, Sam bought $6$ drinks. Grid in 6.

Question 423·Easy·Algebra

Strategy

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