dolphinia

Hint: in any one of the equations, manipulate it to leave an equation that gives one variable in terms of another. Plug this into a different equation. What do you get?

For example, since p+r=8, we know that p=8-r (subtract r from both sides). Plugging this in to p+2q=0 gives 8-r+2q=0.

Doing this will eventually eliminate the variables so you're left with a simpler system.

In each of the equations, manipulate it to get just one variable on one side. Plug the expression back into the expressions.

For example, we know that p/q=5/6. Multiplying boths ides by q, this gives \(p=\frac{5q}{6}\). Plugging this back into \(\frac{p-q}{q-r}\) will give \(\frac{\frac{5q}{6}-q}{q-r}.\)

"The resulting product is less than 500."

Let a and b represent the two primes chosen. The inequality would be \(ab<500\).

You may have already figured that one out, but try using the same method to come up with an inequality for the first part.

Ohh haha I see that now... thanks for correcting me!

Hint: we already know one of the side lengths of the triangle; it's 8. Since it's an equilateral traingle, all of the sides have length 8. Use this along with the area of a triangle formula.