Create equations in two or more variables, graph them, and label axes/scales appropriately.
Write a two-variable constraint for one total
Problem
Adult tickets cost \(\$12\) each, and child tickets cost \(\$8\) each. The total cost is \(\$120\). Let \(a\) be the number of adult tickets and \(c\) be the number of child tickets. Write the ticket-cost constraint.
Big Picture
What this problem is really about
The total comes from two separate ticket categories, so each category needs its own cost contribution. We’ll multiply each ticket price by its matching count, keep those unlike contributions separate, and add them together. Setting that sum equal to the stated total creates one constraint describing every adult-and-child combination with the required cost.
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