**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?

*Answer:* $2.10

*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?

*Answer:* 8:35 pm

*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?

*Answer**:* 6 feet

*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*) = *t*^{2} – 8*t* + 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: 4^{2} – 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

**Answer: (c) 6**