A total item count and a total price give a system of equations: two rules that must both hold. Let one variable count each kind of item. Write one equation for the number sold and another for the dollars earned, then graph both in Desmos and click their intersection. Keep each price with its own item; swapping them describes a different sale.
Hints
- Hint 1
Let count coffees and count muffins. The item total counts each cup and each muffin once. What equation says how many items were sold altogether?
- Hint 2
Each coffee contributes $3 to the money collected, while each muffin contributes $2. Multiply each price by the number sold of that item. What equation gives the total revenue?
- Hint 3
The two equations form a system, meaning both must be true at once. On a graph, their intersection gives both counts. If coffee is , which coordinate of that point answers the question?
Step-by-step
Graph the item and money totals
Step 1Write the item-count equation
Let be the number of coffees and the number of muffins. The 17 items include both kinds, with each item counted once, so .
- Step 2
Write the money equation
The coffees bring in dollars, and the muffins bring in dollars. Count items in the first equation, but count dollars in this one: . Keep the with coffees and the with muffins.
- Step 3
Graph both equations
Type and on separate lines in Desmos. They draw lines with one crossing. A point on either line fits only that line's total; the crossing fits both.
- Step 4
Read the coffee count
Click the intersection, the point where the lines meet. Desmos labels it . The first coordinate is , so the café sold cups of coffee. Choice B.