Answers to Problems of the Week - April 18 to April 24

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: Martin rolls a fair, standard, six-sided die. Match each outcome with its likelihood.

• Martin rolls an even number.                                  • Impossible

• Martin rolls an 8.                                                         • Unlikely

• Martin rolls a number less than 10.                     • As likely as not

• Martin rolls a 1.                                                         • Very likely

• Martin doesn’t roll a 6.                          • Certain.

Solution:  It’s as likely as not that Martin rolls an even number because there are 3 even numbers and 3 odd numbers on a die. It’s impossible that he rolls an 8 because there isn’t an 8 on a die. It’s certain that he rolls a number less than 10 because all the numbers on a die are less than 10. It’s unlikely that he rolls a 1 because only 1 out of 6 numbers on a die is 1. It’s very likely that he doesn’t roll a 6 because 5 out of 6 numbers on a die aren’t 6.

Upper Elementary:

Question: Tara gets to draw one bill at random from either of two buckets. One bucket has 30 $1 bills and 2 $100 bills. Another bucket has 80 $1 bills and 4 $100 bills. Which bucket should Tara choose? Why?

Answer:  Tara should choose the bucket with 30 $1 bills and 2 $100 bills.

Solution:  Since 2 out of 30 + 2 = 32 bills in the first bucket are $100 bills, that means that ²/₃₂ = ¹/₁₆ of the bills are $100. In the other bucket, 4 out of 80 + 4 = 84 bills are $100, so ⁴/₈₄ = 1/21 bills are $100. Since the first bucket has the greater fractional part comprising $100 bills, that’s the smarter bucket to choose.

Middle School:

Question: The ratio of apples to oranges in a box is 7:18. What is the percent chance that a fruit drawn at random from the box will be an orange?

Answer:  72%

Solution:  There are 7 + 18 = 25 fruits in the box. Since 18 out of 25 fruits are oranges and a percentage is out of 100, we can multiply 18 and 25 each by 4 to find the number of fruits out of 100 that are oranges. 18 × 4 = 72, so 72% of the fruits are oranges. If one is chosen at random, then the percent chance that it’ll be an orange is 72%.