A collection of nickels, dimes and quarters is worth $5.30. There are two more dimes than nickels and four more quarters than dimes. How many quarters are in this collection of coins?

 What is the difference between the biggest and the smallest three-digit each formed by different digits?

On average, a human fingernail grows at a rate of 3 mm per month. At this rate, how many total meters will Deshawn’s 10 fingernails grow over the next 10 years? Express your answer as a decimal to the nearest tenth.

Given Parallelogram ABCD. M,N are midpoints of AB,CD. Call E is the intersection of AN and DM , F is the intersection of BN and CM

Show that :

a) \(S_{\Delta MCD}=\dfrac{1}{2}.S_{ABCD}\)

b) \(S_{\Delta MCD}=S_{\Delta NAB}\)

c) \(S_{\Delta EDN}+S_{\Delta FCN}=S_{\Delta EAM}+S_{\Delta FBM}\)

Marita purchased an item for 45% off the original price, plus an additional 20% off the sale price. She also had a $5-off coupon, which the salesclerk applied after these two discounts. Marita’s final purchase price for the item was $50. Assuming she paid no sales tax, what was the original price of the item Marita purchased?

Three numbers have a sum of 5 and the sum of their squares is 29. If the product of the three numbers is –10, what is the least of the three numbers? Express your answer in simplest radical form.

Adam has a triangle with vertices labeled 1 through 3. Jayvon has an octagon with vertices labeled 1 through 8. Each boy starts at position 1 and counts consecutive vertices on his polygon, continuing in the same direction, until he has reached 120 and is back at the vertex labeled 1. Percy did the same activity with his polygon, and he also finished at the vertex labeled 1. If Percy’s polygon is not a triangle or an octagon, what is the sum of all the possible numbers of sides his polygon might have? 

 A bag contains five red marbles, three blue marbles and two green marbles. If six marbles are drawn without replacement from the bag, what is the probability that two marbles of each color are drawn? Express your answer as a common fraction. 

Let there be a pile of  stones. You take the following actions repeatedly until you can no longer repeat them.

1. If you have a pile of  stones, you may divide it into piles of  and  stones.
2. Add  to your running total.

What is the minimum and maximum total you can achieve? Prove that this is the minimum and maximum, and generalize this to any pile of  stones.