Help I Don't Understand?

Question

Their are several questions on this Summer Math packet I do not understand and would be grateful if you could show me all the work, write the answer, and briefly explain how to do the problem.

1.A wholesaler sells coffee at 50 cents a kilogram. She mixes one kind worth 65 cents a kilogram with another worth 40 cents. How much of each kind does she use to make 100kg of the mixture?

2. A specialty food store mixes Brazil nuts and cashews to get mixed nuts, which they sell for $5.00 per kilogram. If the Brazil nuts cost $4.50 per kilogram and the cashews cost $6.00 per kilogram how many kilograms of each should be combined to give 30kg of mixed nuts?

3. Frank needs 5 hours to rake his lawn. But when Sylvia helps him they can do the job in 3 hours. How long would it take Sylvia to rake the lawn by herself?

4.The perimeter of a rectangle is 40cm, and the area is 64cm2. Find the dimensions of the rectangle.

NOTE: I realize I can solve the above problem by guess and check but I was wondering if their is a formula.

5. I am thinking of two consecutive even integers. The sum of their squares is 340. What are the integers.

NOTE: This one is just kind of annoying so if anyone has a quick way of solving this it would be appreciated.

Thank you for your time and if their is anything you need answered please just ask me.

Answer 1

4. The width and length are w and (20-w), not 40 because the perimeter measures the width twice and the length twice.

w(20-w) = 64

20w - w^2 = 64

-w^2 + 20w - 64 = 0

Then factor out to find w, which is your width, and then once you find that solve 20 - w for your length.

5.

Your consecutive even integers are n and n + 2. So from there you can do this:

n^2 + (n+2)^2 = 340

Then factor out (n+2)^2 - I haven't taken math in a couple of years so I'm not positive what the factors are, I wouldn't want to mislead you, but once you do that you should have a slightly different equation on the left and factor out the entire thing.

Sorry I couldn't be more helpful.