Problems of the Week - June 14 to June 20

Rewards for Problems of the week:

5 stars for the correct answer at your level; 10 stars for the next level; 20 stars each for 2+ levels up.

Lower Elementary:

Question: Each soccer team has the following players: 1 goalie, 4 defenders, 4 midfielders, and 2 forwards. How many players are on 10 soccer teams?

Upper Elementary:

Question: Kara and Spencer are practicing their golf swings. They bring 18 golf balls to the course. Kara hits all 18 first, then retrieves all but one. Then it’s Spencer’s turn to hit all the remaining golf balls and retrieve them, but he also loses one. If this pattern continues, who will take the 10th turn, and how many golf balls will he or she hit? Find a way to solve the problem without counting each turn.

Middle School:

Question: Hank and Benjamin play on the same baseball team. Last year, they both had a batting average of .240. Benjamin’s batting average increased by the same amount that Hank’s batting average decreased. If Benjamin has a batting average of .270 this season, then what fractional part of Benjamin’s new batting average is Hank’s new batting average?

Algebra and Up:

Question: Kayla and Margot are both running toward a soccer ball. Kayla is 28 meters away and Margot is 33 meters away. If Kayla can run 2¹/₂ meters per second and Margot can run 2³/₄ meters per second, then how much sooner does the player who reaches the ball first get there?

Challenge problem to take home. 10 stars for the correct answer. 

The perimeter of isosceles triangle ABC is 19. Triangle $$ABD and triangle $$AEC are formed by joining vertices of triangle ABC with the midpoints of their opposite sides.

The perimeter of triangle $$AEC is $$2 units greater than the perimeter of triangle ABD. What is the length of $$BC?