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At a summer camp there is one counselor for every 5 campers. Determine whether there is a direct variation between the number of campers, y, and the number of counselors, x. If so, find the equation of direct variation and you will get 20 points

Respuesta :

texaschic101
campers = y and counselors = x.....1 counselor to 5 campers

y = kx
k = y/x
k = 5/1

y = 5x

lets check..
y = 5x....lets say u have 2 counselors...sub in 2 for x
y = 5(2)
y = 10....so when there is 2 counselors, there are 10 campers

y = 5x...lets say u have 3 counselors...sub in 3 for x
y = 5(3)
y = 15...so when there are 3 counselors, there are 15 campers

2/10 reduces to 1/5
3/15 reduces to 1/5

so yes, this is a direct variation with ur equation being y = 5x

x =(1/5)y  is the equation for direct variation.

What is direct variation ?

The relationship between two variables in which one is a constant multiple of the other is known as direct variation.

When one variable affects the other, for example, they are said to be proportional. The equation b = ka is used when b is directly proportional to a. (where k is a constant).

It is given that

At a summer camp there is one counselor for every 5 campers.

Let us consider no. of counselor = x

No. of campers = y

the number of counselors is dependent upon the number of campers

x ∝ y

x = ky

where k is the proportionality constant

x = 1 for y = 5

k = 1/5

x =(1/5)y

This is the equation for direct variation.

To know more about direct variation

https://brainly.com/question/14254277

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