Practice Problems:
Problem Solving
5th Grade
1. In the big Beantown Spitting Contest, the prizes were given out in the following manner. First place spitter received a prize of $10. Second
place spitter received $8. Third place spitter received $6. This pattern continued all the way down to the spitter that was in 5th place. Mr. Pepper provided the money for this event. How much money in all did Mr. Pepper give out for all of the winners?
2. In the big Beantown Arm Wrestling Championship, there will be 8 contestants. Each contestant will arm wrestle every other contestant 1 time. We will then tally up how many wins and losses each contestant has to determine the winner. For each individual contest, we will have to use a brand new towel to clean up the sweat. How many towels will we need in
all?
1. Mrs. Radish invented a new game. She tied Abe to the wall and let the kids throw pies at him. If you hit him in the head, you scored 3 points.
If you hit him anywhere else, or even if you missed, you scored 2
points. Bertha was the first person to try. She took 3 throws
and scored a total of 6 points. Was she able to hit Abe in the head?
2. There were 16 people hiding in a closet in Mrs. Cauliflower’s room.
She opened the door and screamed, causing ½ of the people to run
away. The next time she opened the door, ½ of the people that were remaining in the closet ran away. This happened one more time.
She screamed and ½ of the people left in the closet ran away.
At this point, how many people are left in the closet?
1. Angie paints fingernails and toenails for a living. On each fingernail and toenail she paints full copies of great works of art. She specializes in the works of Picasso, Van Gogh, and Mrs. Broccoli. In one day she painted a
total of 100 nails. If she did all of the toenails and all of the fingernails of each person, how many people in all did she paint that day?
2. One of Angie’s customers that day, Fred, not only wanted his nails painted, but he also wanted little picture frames around them as well. Angie charged him $5 per frame for Picasso copies, $10 per frame for the works of Van Gogh, and no charge for the works of Mrs. Broccoli. One foot alone cost Fred $40 just for the frames, and he got no works of Mrs. Broccoli on that foot. How
many Picassos and Van Goghs did Fred get on that one foot?
5th Grade
1. In the big Beantown Spitting Contest, the prizes were given out in the following manner. First place spitter received a prize of $10. Second
place spitter received $8. Third place spitter received $6. This pattern continued all the way down to the spitter that was in 5th place. Mr. Pepper provided the money for this event. How much money in all did Mr. Pepper give out for all of the winners?
2. In the big Beantown Arm Wrestling Championship, there will be 8 contestants. Each contestant will arm wrestle every other contestant 1 time. We will then tally up how many wins and losses each contestant has to determine the winner. For each individual contest, we will have to use a brand new towel to clean up the sweat. How many towels will we need in
all?
1. Mrs. Radish invented a new game. She tied Abe to the wall and let the kids throw pies at him. If you hit him in the head, you scored 3 points.
If you hit him anywhere else, or even if you missed, you scored 2
points. Bertha was the first person to try. She took 3 throws
and scored a total of 6 points. Was she able to hit Abe in the head?
2. There were 16 people hiding in a closet in Mrs. Cauliflower’s room.
She opened the door and screamed, causing ½ of the people to run
away. The next time she opened the door, ½ of the people that were remaining in the closet ran away. This happened one more time.
She screamed and ½ of the people left in the closet ran away.
At this point, how many people are left in the closet?
1. Angie paints fingernails and toenails for a living. On each fingernail and toenail she paints full copies of great works of art. She specializes in the works of Picasso, Van Gogh, and Mrs. Broccoli. In one day she painted a
total of 100 nails. If she did all of the toenails and all of the fingernails of each person, how many people in all did she paint that day?
2. One of Angie’s customers that day, Fred, not only wanted his nails painted, but he also wanted little picture frames around them as well. Angie charged him $5 per frame for Picasso copies, $10 per frame for the works of Van Gogh, and no charge for the works of Mrs. Broccoli. One foot alone cost Fred $40 just for the frames, and he got no works of Mrs. Broccoli on that foot. How
many Picassos and Van Goghs did Fred get on that one foot?