A change in survey percentages is a percentage-point change when the number of people surveyed stays fixed. Subtract the percentages to find what share of the whole the added people represent, then use a part-whole equation in Desmos to find the total. The trap is treating the added people as the entire original group rather than only the increase.
Hints
- Hint 1
The whole is the group that counts as . The 12 additional online choices come from students already surveyed, so the whole stays the same. What share of that whole do those 12 students represent?
- Hint 2
A percentage-point difference comes from subtracting the two percentages. That difference describes the 12 additional students, not everyone who prefers online resources. How can you write that part as a percent of the unknown total?
- Hint 3
Let count all students surveyed. In a part-whole equation, the part equals a percent of the whole. Set the percent difference of equal to , then solve for .
Step-by-step
Use the percent difference
Step 1Find the added share
The whole is everyone surveyed. Twelve students change their choice, but the total surveyed stays the same, so subtract the two online percentages:
When the whole stays fixed, the difference in percentages is the share represented by the added people.
- Step 2
Connect the added students to the total
Let be all students surveyed. The 12 additional online students make up of that whole, so the part-whole equation is:
Don't add to the total: the survey didn't gain students.
- Step 3
Solve for the number surveyed
Type . Use instead of and instead of so Desmos finds the unknown rather than graphing the equation. Under PARAMETERS, it shows . Since counts everyone surveyed, 240 students were surveyed. Grid in 240.