A juice bar sells two sizes of fruit smoothies. A small smoothie costs $4.50, and a large smoothie costs $6.00. On a busy afternoon, the bar sold a total of 120 smoothies and collected $615 in sales.
Based on this information, how many small smoothies were sold?
Two sizes, a total number sold, and a total collected point to a system of equations: two equations about the same two unknown quantities. Write one equation for the smoothie count and another for the money. Then graph both in Desmos and click where the lines cross. Keep track of which size you assigned to so you don't choose the wrong coordinate.
Hints
- Hint 1
The total count includes both sizes. If counts small smoothies and counts large smoothies, their counts add to the total sold. What equation does that give you?
- Hint 2
Revenue means money collected. Multiply each size's price by the number sold, then add the two amounts. Keep each price with its own size. What must that sum equal?
- Hint 3
An intersection is where two lines cross. Its coordinates make both equations true. After you click it in Desmos, which coordinate counts the small smoothies?
Step-by-step
Graph the count and sales equations
Step 1Write the smoothie-count equation
Let be the number of small smoothies and the number of large smoothies. Every smoothie sold was one size or the other, so the total count gives .
- Step 2
Write the sales equation
Small smoothies bring in dollars, and large smoothies bring in dollars. The bar collected $615, so . The count equation adds smoothies; the sales equation adds dollars. Don't pair a price with the other size.
- Step 3
Read the small-smoothie count
Type and on separate lines in Desmos. Click their intersection, the point that satisfies both equations. Desmos shows . The first coordinate is , so the bar sold small smoothies; counts the large ones. Choice C.