What's the value of k and p?
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We know that:

y = -5.797

x = 4.0

and:

k/y = p/x + 1

We can rewrite this as:

k = (p/x + 1)*y = p*(y/x) + y

Replacing the values of x and y, we get:

k = p*(-5.797/4.0) + (-5.797)

We could simplify this to get:

k = p*(-1.44925) - 5.797

So we ended with a linear equation, so for a given value of p, we know the k.

Now, we could solve this if we add the restriction that k and p must be integers.

Then we can return to:

k = (p/x + 1)*y = (p + x)*(y/x)

replacing the values we get:

k = (p + 4.0)*(-5.797/4.0)

if p = 3996, then p + 4 = 4000

and 4000*(-5.797/4.0) = 1000*(-5.797) = -5797

Then if we take p = 3996, k will also be an integer:

k = (3996 + 4.0)*(-5.797/4.0) = -5797

Then:

p = 3996

k = -5797

is a possible solution of the problem.

entering that problem on the tube might get you an answer