Modeling Linear Systems Graphically

Question

The school is selling tickets to a choral performance. On the first day of ticket sales, they sold 6 child tickets and 10 adult tickets for a total of $150. The school took in $135 on the second day by selling 15 child tickets and 5 adult tickets. Find the price of an adult ticket and the price of a child ticket.

How do I graph this?

Answer 1

You set up a system of equations, one for the revenue on day 1 and another for day 2.

Day 1: 6c + 10a = 150 (c = price of child's ticket; a = price of adult's ticket)

Day 2: 15c + 5a = 135

These can be solved by elimination or substitution, but they specify graphing.

As they are straight lines, the easiest way is to find two points on the graph for each equation and draw a line between them.

Easiest way to do that is to set c = 0 and solve for a, then set a = 0 and solve for c for each equation.

Ex: Day 1: 6(0) + 10a = 150, so a = 15 (point 0,15); 6c + 10(0) = 150, so c = 25 (point 25,0).

When both lines are drawn, intersection is the solution. Check with Desmos Graphing Calculator website.