Ruth is starting a summer camp for children who are deaf or hard of hearing. She needs to hire enough counselors to chaperone the children. There is a proportional relationship between the number of counselors Ruth hires, x, and the maximum number of children who can attend the camp, y.

Question

By law, if Ruth hires 2 counselors, then at most 10 children can attend the camp. Write the equation for the relationship between x and y.

Answer 1

Let x represent the number of counselors and y represent the maximum number of children who can attend the camp.
Since there is a proportional relationship between x and y, we can write the equation as:
y = (number of children per counselor) * x
Given that if Ruth hires 2 counselors, at most 10 children can attend the camp, we have:
10 = (number of children per counselor) * 2
To find the number of children per counselor, we divide both sides of the equation by 2:
10/2 = (number of children per counselor)
5 = (number of children per counselor)
Therefore, the equation for the relationship between x and y is:
y = 5x