Question 603·Easy·Algebra

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The graph shows the possible combinations of the number of bags of popcorn, $x$ , and the number of drinks, $y$ , that could be purchased for $30 at a movie theater. If Jordan’s total purchase was $30 and included $3$ bags of popcorn, how many drinks did Jordan purchase?

The cue is a linear graph: each point on the straight line gives one possible pair of purchases. Start with the given number of bags on the horizontal axis, then find the matching number of drinks. If that point isn't labeled, use the line's endpoints: halfway across means halfway between their heights. The vertical intercept describes a purchase with no popcorn.

Hints

Hint 1
An ordered pair $(x,y)$ lists the horizontal value first. Here, that value counts bags of popcorn. Find $x=3$ on the horizontal axis; where does it fall between the line's endpoints?
Hint 2
A straight line changes evenly: equal moves across it give equal changes in height. At the horizontal midpoint, how much of the line's total drop has happened?

Step-by-step

Read the midpoint of the line
Step 1
Locate Jordan's number of bags
No Desmos needed. The given graph already shows the purchase combinations. The horizontal axis counts bags, and the line runs from $(0,10)$ to $(6,0)$ . Find the midpoint of its horizontal span:
$\frac{6}{2}=3.$
So Jordan's $x=3$ is halfway between the endpoints.
Step 2
Read the matching number of drinks
A straight line changes evenly, so $y$ is halfway between $10$ and $0$ here. Halfway across a straight line means halfway between its heights. Take half of $10$ :
$\frac{10}{2}=5.$
Since $y$ counts drinks, Jordan purchased $5$ drinks. Choice B.

Lessons that teach this

SAT AlgebraIntermediateCoreRead and write two-variable linear equations

Question 603·Easy·Algebra

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