A one-variable equation fits a story with an amount given to each person, an amount left over, and an original total. Multiply the per-person amount by the number of people, then add the leftovers to recover the total. A Desmos regression can solve the equation. Dividing the original total by the per-person amount incorrectly counts the leftovers as handed out.
Hints
- Hint 1
Let a variable count the students. If each student gets pens, multiply by that variable to count all the pens handed out.
- Hint 2
The remainder is what wasn't handed out. Add the 8 pens left over to the pens given to students. What should that sum equal?
Step-by-step
Model the pens, then solve in Desmos
Step 1Write an equation for all the pens
Let be the number of students. Giving pens to each student uses pens. The 8 remaining pens weren't given out, so add them once to account for all purchased:
Pens handed out plus pens left over equals pens purchased. Dividing by would count the leftover pens as if students received them.
- Step 2
Find the number of students
Type in Desmos. Replace with and with : this tells Desmos to find the value that makes the two sides equal, rather than graphing . Under PARAMETERS, Desmos shows . Since the variable counts students, there are students in the class. Choice B.