A fixed budget for two kinds of tickets gives a two-variable linear equation: each ticket price times its ticket count adds to the total. Use a labeled point on the graph as a test pair, and evaluate the choices in Desmos. Keep the coordinates in order and check both sides of each equation; the right ticket prices with the wrong total still won't fit.
Hints
- Hint 1
An ordered pair lists first, then . At the labeled point , there are adult tickets and child tickets. A matching equation must work for those counts in that order.
- Hint 2
In a budget equation, a number multiplying a ticket count is the price of one ticket. Use the labeled point to calculate the total for each arrangement of the two prices. Which arrangement reaches the full budget?
- Hint 3
The right side of an equation matters too. For a choice written as , put in the point's -value and check whether it gives the point's -value.
Step-by-step
Test a labeled point
Step 1Read the point as a ticket mix
The marked point means adult tickets and child tickets. A solution to a graphed equation is a point that makes it true, so the equation you choose must work for this pair. Keep the coordinates in order.
- Step 2
Test the two ticket-price arrangements
Type and , then evaluate and . Desmos prints and , respectively. Each number multiplying a ticket count is a price per ticket, so swapping the prices misses the $170 budget.
- Step 3
Check the total on the other equation
The equation with on the left and on the right has the wrong total. At , its left side is , not . A point on a graph must make both sides of its equation equal.
- Step 4
Check the remaining form and choose
For the equation written as , type . Desmos prints about , but the marked point has when . So represents the budget: $3 per adult ticket and $4 per child ticket. Choice A.