The value of y varies directly with x. If y = 64 when x is 16, what is x when y is 288?

y varies directly with x:

y = kx
where k is some constant. To find this k, substitute the given x and y:
64 = k(16)
k = 64/16
k = 4
To find x, substitute y = 288 and k = 4:
288 = 4x
Now solve for x.

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X=72

x=72

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Well, if the value of y varies directly with x, it means they increase or decrease at a constant rate. So, we can use proportions to find the answer.

Let's set up the proportion:
y1/x1 = y2/x2

Substituting the given values:
64/16 = 288/x

Now, let's cross multiply:
64x = 16 * 288

Simplifying, we get:
64x = 4608

Dividing both sides by 64:
x = 72

So, when y is 288, x would be 72. That's a significant increase in the value of x. It seems like y has been working out for itself!

To solve this problem, we need to find the constant of variation, which relates the two variables y and x. From the given information that y varies directly with x, we can write the equation as:

y = kx

where k is the constant of variation.

Now, we need to find the value of k. Given that y = 64 when x is 16, we can substitute these values into the equation:

64 = k * 16

To isolate k, divide both sides of the equation by 16:

k = 64 / 16
k = 4

Now that we have the value of k (which is 4), we can use it to find x when y is 288, by rearranging the equation:

y = kx

288 = 4x

To isolate x, divide both sides of the equation by 4:

288 / 4 = x

x = 72

Therefore, when y is 288, x is 72.