T101 Problem Solving Worksheet

DIRECTIONS: With your partner, show all work on the same separate sheet of paper.

Answer the question on the other sheet of paper. Circle your final answer.

1. A farmer looks out into the barnyard and sees the pigs and the chickens. He says to his daughter, “I count 169 heads and 398 feet. How many pigs and how many chickens are out there?

2. If you have a bunch of 10 cent and 5 cent stamps, and you know that here are

20 stamps and their total value is $1.50, how many of each do you have?

3. Let’s say you are building a patio in your back yard. You have decided to make

the patio 12 feet by 9 feet. The local building supply store sells bricks that are

6 inches by 4 inches for 25 cents each. How much will the patio cost?

4. I had some pennies, nickels, dimes and quarters in my pocket. When I reached in

and pulled out some change, I had less that 10 coins whose value was 42 cents.

What are all the possibilities for the numbers of coins I might have in my hand?

5. Five people enter a racquetball tournament in which each person must play every

other person once. Determine the total number of games that will be played.

6. Mark planted 14 rows of apple trees, and each row had 21 trees. If each tree

yielded and average of 200 apples, how many apples grew in the orchard?

7. Find a two-digit number that, when added to its reverse, is the closest to 130. Show your work.

8. When two numbers are multiplied, their product is 759, but when one is subtracted from the other their difference is 10. What are these two numbers?

9. Suppose that you have a supply of red, blue, green and yellow square tiles. What is the fewest number of different colors needed to form a 3 x 3 square of tiles so that no tile touches another tile of the same color along an entire edge?

10. Tom had 6 more red tiles than yellow tiles. He gave half of his red tiles to Amy and half of his yellow tiles to Ray. If Ray has 7 yellow tiles, how many tiles does Tom have?

11. Four people want to cross the river. There is only one boat available and it can carry a maximum of 200 pounds. The weights of the four people are 190,170, 110, and 90 pounds. How can they all manage to get across the river, and what is the minimum number of crossings required for the boat?

12. A special rubber ball is dropped from the top of a wall that is 16m high. Each time the ball bounces, it rises half as high as the distance it fell. The ball is caught when it bounces 1 meter high. How many times did the ball bounce?

13. Linda picked a basket of apples. She gave half of the apples to a neighbor, then 8 apples to her mother, then half of the remaining apples to her best friend, and kept the 3 remaining apples for herself. How many apples did she start with in the basket?

ANSWERS

1. 30 pigs and 139 chickens 2. Ten 10 cent and ten 5 cents

3. $162 4. 2p, 0n, 4d, 0q: 2p, 2n, 3d, 0q:

2p, 4n, 2d, 0q: 2p, 6n, 1d, 0q

2p, 3n, 0d, 1q; 2p, 1n, 1d, 1q;

7p, 0n, 1d, 1q

5. 10 games 6. 58,800 apples

7. 75 + 57, 84 + 48, 93 + 39 8. 23 and 33

9. 3 different colors 10. 34 tiles

11. 9 crossings 12. 4 bounces

13. 28 apples