4.1 There are 30 people sitting at a round table. Some of them are liars, the others tell the truth. We know that out of the two neighbours of every liar, exactly one is a liar. Each of the 30 people is asked how many liars are sitting next to them. 12 say exactly one and the others say that both of their neighbours are liars. How many liars are there around the table?

Please don't provide handwritten solution.....

2. You have some coins, each of which is a penny (1 cent), a nickel (5 cents), a dime (10 cents), or a quarter (25 cents). You know that • you have twice as many pennies as nickels, • the number of dimes is one more than the number of pennies and nickels combined, you have 34 coins in total, • and the total value of your coins is $2.70 (270 cents). (a) Set up a system of linear equations for the numbers of pennies, nickels, dimes, and quarters you have. (b) Determine how many coins of each type you have, by solving the system from part (a).

3.) Mr. Richards and Mr. Dolge each began improving their yards over the summer by buying bags of soil (fancy dirt) and bags of mulch (bark dust). Since Mr. Dolge has access to a truck, Mr. Richards got a ride and as a result they got their supplies from the same store. Mr. Dolge spent $97 on 3 bags of soil and 14 bags of mulch. Mr. Richards got 14 bags of soil and 7 bags of mulch for $161. They forgot to get a receipt, but just in case they need more supplies, they are wondering how much each bag of soil will cost, and how much each bag of mulch will cost. What should they find these prices to be?