Question 121·Easy·Linear Equations in Two Variables
The graph shows the possible combinations of the number of bags of popcorn, , and the number of drinks, , that could be purchased for $30 at a movie theater. If Jordan’s total purchase was $30 and included bags of popcorn, how many drinks did Jordan purchase?
When a graph shows all combinations of two items that total a fixed amount, you can either read the needed coordinate directly from the graph (plug in the given and find the matching ) or write a linear equation for the total and substitute the given value.
Hints
Read the point on the line
Find the point on the line directly above and read its -value.
Think in dollars
Three bags of popcorn cost some of the $30. The rest of the money is spent on drinks.
Use an equation if you prefer
A point on the graph represents a total cost of $30. You can model it with a linear equation like and substitute .
Desmos Guide
Graph the line
Enter .
Mark
Enter the vertical line .
Find the intersection
Click the intersection point of the two graphs. The -coordinate of that point is the number of drinks purchased.
Step-by-step Explanation
Write an equation from the intercepts
The line passes through and . That means $30 buys either bags of popcorn (so popcorn is $5 each) or drinks (so drinks are $3 each). Therefore, the total-cost equation is .
Substitute and solve
Substitute into :
so and . Therefore, Jordan purchased 5 drinks.