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If y varies directly as x, and y is 180 when x is n and y is n when x is 5, what is the value of n? 6 18 30 36

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Answer:
If y varies directly as x, then we can write the relationship between y and x as y = kx, where k is a constant of proportionality. To find the value of k, we can use the information given in the problem.

We know that when y is 180 and x is n, we have:

180 = kn

Similarly, when y is n and x is 5, we have:

n = k(5)

To solve for k, we can divide the first equation by the second:

180/n = k(5)/n

Simplifying this expression, we get:

36 = k

Now that we know the value of k, we can use either of the two equations we wrote earlier to solve for n. Let's use the second equation:

n = k(5) = 36(5) = 180

Therefore, the value of n is 180.

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