There are two ways to have 30 cents using six coins, either six nickels or one quarter and five pennies. For each of thecombinations of coins given, find the minimum n such thatn(middle value coin) = (n – k)(largevalue coin) + k(small value coin).

Find the minimal number of dimes that can be replaced with anequal number of quarters and pennies combined.

Answer:_____________________________________________________

Find the minimal number of dimes that can be replaced with an equal number of quarters and nickels combined.

Answer:_____________________________________________________

Find the minimal number of nickels that can be replaced with anequal number of dimes and pennies combined.

Answer:_____________________________________________________

We have three types of birds at three prices: The large birdcosts 3 coins, the middle sized bird costs 2 coins and four chickscost 1 coin. Find the Diophantine solutions for 100 birds for 100coins, where the number of every kind of bird is a non-negativeinteger.

Write the equation for large birds in terms of chicks:_________________

Write the equation for middle sized birds in terms of chicks:_________________

What is the lower limit for the number of chicks? _________

What is upper limit for the number of chicks? _________

Find the four positive integer solutions of 100birds for 100 coins. (The solution where there are 0 large birds or0 middle sized birds do not count.)

Solution #1 = [____ __________] Solution #2 = [____ _____ _____]

Solution #3 = [____ __________] Solution #4 = [____ _____ _____]