Algebraic Expressions & Equations
While there were many problems written and solved for MATHCOUNTS in 2019, below is a selection of some of the best of the year!
2018-2019 School Handbook, #27
A segment with endpoints G(-2, 3) and H(4, 7) is dilated by a scale factor of 2/3 with center of dilation (0, 0). What is the sum of all the coordinates of G’ and H’?
Millions of people will fix their eyes on the ball dropping in Times Square this New Year’s Eve to indicate the end of 2019 and the beginning of 2020. The famous ball is six feet in diameter and weighs 1070 pounds. If the weight were distributed evenly throughout the ball, what would be the average number of pounds per cubic foot, to the nearest tenth? (Assume that the ball is a perfect sphere, though its surface is actually made up of 504 small, crystal triangles.)
A local charity is wrapping holiday gifts for local needy families. When 8 volunteers work together, they can get all of the gifts wrapped and distributed in 6 hours. How many hours would it have taken if there had been 12 volunteers, each working at the same rate?
Abby, Brenda, Celia, Denise and Elizabeth are going to their town’s annual hayride. Tickets cost $8.00 for people 12 years old and older but only $5.00 for people 11 years old and younger. The total price for their five tickets is $31.00. How many people in the group are 12 years old or older?
Bethany and her family are attending the Funville Town Fall Festival, and the first thing they do is get in line for the Maize (corn) Maze. When Bethany gets to the entrance of the Maze she is facing north. Following the paths, she walks straight ahead for 10 feet and reaches an intersection at which she turns right and walks 40 feet east, at which point the path dead ends. Bethany decides to back-track 15 feet and turns south. She walks 5 feet south and then turns and walks 6 feet east. If Bethany was to walk straight back to the entrance, cutting through the corn
The ratio of girls to boys in Mrs. Franks’ 7th grade class is ¾ (excluding Mrs. Franks). On Monday, 4 girls and 6 boys got to go on a special field trip for honor roll students. Since no other students were absent on Monday, the ratio of girls remaining in the class to boys remaining in the class was 4/5. How many students are in Mrs. Franks’ class when everyone is present?
After polling each student in her homeroom about their summer plans, Mrs. Baker discovered that each student planned to participate in one or more of the following activities:
This summer Owen and Jack will both have part time jobs. Owen will be working as a lifeguard and Jack will be working as a server at a local restaurant. Owen plans to work 15 hours each week and will be making $7 per hour. Jack will make an hourly rate of $2.10 plus 18% of his sales in tips. If Jack averages $30 in sales per hour, how many hours will he need to work in order to make the same amount per week as Owen?
Thursday is the 4th of July... here are a few problems relating to Independence Day!! While walking around at their town’s Independence Day Festival, Latrease and Hannah decide to buy lunch. Latrease bought two hot dogs and a soda for a total of $7.50. Hannah bought a hot dog, a soda, and a bag of chips for $5.50. If a bag of chips costs $1.00, how much does one hot dog cost?
In the summer months, a common problem people suffer from is dehydration – not enough water in their body. Waiting until you feel thirsty is not a good indicator that it’s time to drink water. In fact, once thirst has settled in, you are already dehydrated! A general guideline is that people should drink eight 8-ounce glasses of water per day. According to this guideline, how many gallons of water should a person drink in a day, given that 1 gallon = 4 quarts and 1 quart = 32 ounces? Express your answer as a decimal to the nearest tenth.