A linear system is two equations about the same unknown counts. A total earned and a comparison between counts are your cues to write one money equation and one count equation, then graph both in Desmos and click where they cross. Match each coordinate to its count; the tempting slip is to report the first coordinate without checking what it represents.
Hints
- Hint 1
The revenue, or money earned, from each kind of print is its price times the number sold. What expression gives the dollars from small prints, and what expression gives the dollars from large prints?
- Hint 2
The phrase 9 more large prints compares the numbers of prints, not the money earned. The large-print count equals the small-print count plus . Which variable stands for each count?
- Hint 3
An intersection is where two lines cross. That point makes both equations true, but its two coordinates represent different counts. Which coordinate will answer the question?
Step-by-step
Model both facts and read the intersection
Step 1Write the money equation
The problem uses for small prints and for large prints. Small prints earn $4 each, so they bring in dollars; large prints earn $7 each, so they bring in dollars. Their combined earnings are $250, so .
- Step 2
Write the count equation
Nine more large prints means the large-print count is the small-print count plus : . Reversing this to would say the studio sold more small prints instead.
- Step 3
Read the large-print count
Type and on separate Desmos lines. Click their intersection, where both facts hold. Desmos shows : small prints and large prints. Read the coordinate that matches the count asked for. The studio sold large prints. Grid in 26.