2 people = 18 tacos per person
3 people = 12 tacos per person
4 people = 9 tacos per person
6 people = 6 tacos per person
The text above shows how 36 tacos can be divided equally among different numbers of people.
Answer both of the following questions:
1. Is this situation an example of direct variation, inverse variation, or neither? Explain your reasoning.
2. Write an equation to model this situation. Reminder: You must show the process as well as the correct answer using algebraic work.
1. This situation is an example of inverse variation. Inverse variation occurs when one quantity increases while the other quantity decreases in a predictable way. In this case, as the number of people increases, the number of tacos per person decreases.
2. To write an equation to model this situation, let's use the variable "t" to represent the number of tacos and "p" to represent the number of people.
From the information given, we can find a pattern in the relationship between the number of tacos and the number of people. The product of the number of tacos and the number of people is always constant.
For 2 people, the number of tacos per person is 18, so we have 2 * 18 = 36 tacos in total.
For 3 people, the number of tacos per person is 12, so we have 3 * 12 = 36 tacos in total.
For 4 people, the number of tacos per person is 9, so we have 4 * 9 = 36 tacos in total.
For 6 people, the number of tacos per person is 6, so we have 6 * 6 = 36 tacos in total.
Based on this pattern, we can write the equation as:
t * p = k
where t is the number of tacos, p is the number of people, and k is a constant value.
Therefore, the equation to model this situation is tp = 36.