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This week's Critical Math is all about multi-step problem solving. Be sure to check your work before looking at those answers!
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?
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?
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?
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?
Answers Below!
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) = 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.
