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?

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asked Aug 26, 2020 4.3k views

2 Answers

Ruvi · Answer 1 · 2020-09-02T12:35:41+0000

For this case we have that if "y" varies directly with "x", we can propose:

y = kx

Where "k" represents the constant of proportionality.

According to the data:

$180 = kn\\n = k5$

We substitute the second equation in the first:

$180 = k * k5\\180 = 5k ^ 2\\k ^ 2 = \frac {180} {5}\\k ^ 2 = 36$

We apply root:

$k = \pm \sqrt {36}\\k = \pm6$

If k = 6, then
n = 6 * 5 = 30

Answer: