# Answers to Problems of the Week - May 9 to May 15

May 15, 2022 | Lake Boone

Rewards for Problems of the week:

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

Lower Elementary:

Question: Kylie sold books at a yard sale for 10¢ each and toys for 50¢ each. If she sells 6 books and 3 toys, how much does Kylie earn altogether?

Solution:  Kylie earned 10¢, 6 times for the books. That’s 10, 20, 30, 40, 50, 60¢. She earned 50¢, 3 times for the toys. That’s 50, 100, 150¢, or \$1.50. So, altogether, Kylie earned \$1.50 + \$0.60 = \$2.10.

Upper Elementary:

Question: Eight groups of children are performing skits at their summer camp comedy show. Each skit is 5 minutes long. If each group performs once and the campers must be done with the comedy show by 9:15 pm, then what is the latest time they can start the show?

Solution:  The amount of time is takes for all of the groups to finish their skits is 8 × 5 = 40 minutes. Since they have to finish the show by 9:15 pm, we count back 40 minutes before 9:15 pm to 8:35 pm.

Middle School:

Question: A 9-foot tree casts a 6-foot shadow. Cameron’s dog casts a 2-foot shadow. Cameron is twice as tall as the dog. How tall is Cameron?

Solution:  The tree’s shadow’s length is two-thirds the height of the tree. So, the length of the dog’s shadow is two-thirds its height; 2 feet is two-thirds of 3 feet, so the dog must be 3 feet tall. That means that Cameron is 6 feet tall because he’s twice as tall as the dog.

Algebra and Up:

Question: The profit earned by a coffee company, measured in thousands of dollars, is modeled by the function f(t) = t2 – 8t + 16, wherein t is measured in months and t = 1 is January 2012. What month does the coffee company earn the least amount of money? How much do they earn?

Answer:   The coffee company earned \$0 in April.

Solution:  This function is a parabola that opens upward, so the lowest value is at the vertex. To find the month, we find b/2a = –8/–2 = 4. So, the vertex is at t = 4, which represents the month of April. To find how much they earned, we set t = 4 and solve: 42 – 8(4) + 16 = 16 – 32 + 16 = 0. So, they earned \$0 in April.

## Challenge problem to take home. 5 stars for the correct answer.

Which of the numbers below can't you get by changing some of the `+` to `-`?

a) -8              b) 0          c) 6           d) 8