Answers to Problems of the Week - January 17 to January 23

Lower Elementary:

Question: Mila grows red, pink, and yellow roses in her garden. She has a total of 18 rose bushes. Half of the rose bushes grow red roses, six of them grow pink roses, and the rest grow yellow roses. How many yellow rose bushes does Mila have?

Answer:  3 yellow rose bushes

Solution:  If Mila has 18 rose bushes in total and half of them grow red roses, then she has half of 18 = 9 red rose bushes. To find the number of yellow rose bushes, we subtract the other rose bushes: 18 – 9 – 6 = 3 yellow rose bushes.

 Upper Elementary:

Question: It costs Hank $23 to buy tulip bulbs for his garden. With those bulbs, he grows 160 tulips. He sells each tulip for 85¢. How much money does Hank make in profit?

Answer:  $113

Solution:  Hank gets $0.85 × 160 = $136 for all his tulips. Since he spent $23 to get the bulbs, his profit is $136 – $23 = $113.

Middle School:

Question: An orange tree grows at a rate of 8 millimeters per month. What is its growth rate in centimeters per year?

Answer:  9.6 centimeters per year

Solution:  There are 12 months in a year. In a year, the tree grows 8 millimeters, 12 times, or 96 millimeters. Since there are 10 millimeters in a centimeter, the tree grows 9.6 centimeters per year.

Algebra and Up:

Question: The population of trillium flowers in a state park over a number of years can be modeled by the function f(t) = 1,024(2)^–2t, wherein t is the number of years that have passed since 2010. When was the population of trillium flowers equal to 1?

(Hint: t is an integer.)

Answer:  2015

Solution:  The function for the population is f(t) = 1,024(2)^–2t. Since we want to know how many years passed until the population was 1, we set the function equal to 1 and solve for t. Since we know t is an integer, one way to solve this problem is to plug in values and find that t = 5. It will take 5 years for the population to decrease to 1. Since t is the number of years since 2010, the population was 1 in 2015.