## Problem Solving

Choose five of the following six problems to solve and explain on your own paper

1. Alexander, David, Connor, Zachary, Michael, and Jacob each gave one Valentine’s Day card to a girl in their class. The girls Alyssa, Stephanie, Alexandra, Alexis, Jordan, and Emma each received one Valentine’s Day card and want to know who gave it to them. Be sure to list your answer.

a. David likes Emma and Alexis. He gave a card to one of them.
b. Jordan heard Connor say that he did not give a card to Alyssa.
c. Zachary gave Stephanie a card.
d. Alyssa heard Michael say that he did not give a card to Emma.
e. Jordan heard Jacob say that he did not give a card to Emma.
f. Connor did not give a card to Alexis.
g. Michael could not decide whether to give a card to Jordan or to Alexis. They are both nice, and he likes to talk to both of them. Since he couldn’t decide, he decided to give a card to someone else on Valentine’s Day!
h. David did not give a card to Alyssa.
i. Jordan knows that either Michael or Alexander gave her a card.
j. Alyssa knows that either David or Jacob gave her a card.

2. Matt Tress found 46 cents under his bed. He had less than 11 coins and one of the coins was a quarter. What is the number of combinations of coins he could have?

3. Artie Choke and Tom A. Toe both shop at the same local grocery store between five and six in the evening. The last time they saw each other was on Tuesday. Artie shops every five days and Tom shops every four days. What day of the week will they next run into each other at the store, assuming that the store is open seven days a week?

4. In driving from town A to town D, you pass first through town B and then through town C. It is 10 miles farther from A to B than from B to C and 10 miles farther from B to C than from C to D. If it is 390 miles from A to D, how far is it from A to B?

5. A businesswoman went to the bank and sent half of her money to a stockbroker. Other than a \$2 parking fee before she entered the bank and a \$1 mail fee after she left the bank, this was all the money she spent. On the second day, she returned to the bank and sent half of her remaining money to the stockbroker. Once again, the only other expenses were the \$2 parking fee and the \$1 mail fee. If she had \$182 left, how much money did she have before the trip to the bank on the first day? Careful: Work in the order things happened not in the order listed.

6. How can you measure 1 liter of water from a faucet if you have only a 4-liter unmarked container and a 7-liter unmarked container?