A total number of items and a separate cost total call for a system of equations: two equations using the same unknowns. Keep the bottle count and the dollar total in separate equations. Graph both in Desmos and click their intersection, which satisfies both facts. Then check which coordinate represents the item the question asks for.
Hints
- Hint 1
In a system of equations, each total gets its own equation. The bottle total counts one for every bottle of water or juice, regardless of price. What do and add up to?
- Hint 2
For the cost equation, multiply each price by the number of bottles at that price. The water price goes with , and the juice price goes with . What must their combined cost equal?
- Hint 3
The intersection of the two graphed equations makes both totals true. If you use for water and for juice in Desmos, the second coordinate gives which count?
Step-by-step
Graph the count and cost equations
Step 1Write the bottle-count equation
The 8 bottles are all water or juice, so adding their counts gives the count equation:
- Step 2
Write the cost equation
Each water bottle costs $2, so water bottles cost dollars. Each juice bottle costs $3, so juice bottles cost dollars. Together, they cost $18, giving the cost equation:
- Step 3
Read the juice count from the intersection
For Desmos, use and . Type and on separate lines. Click their intersection, the point that satisfies both equations. Desmos shows . The second coordinate is , so Jamie buys bottles of juice. Choice B.