Answers to Problems of the Week - October 26 to October 31

Rewards for Problems of the week:

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

Lower Elementary:

Question: Tori has reading homework that is 19 pages long. The homework is printed front-and-back on sheets of paper. How many sheets of paper are needed for the whole reading assignment?

Answer:  10 sheets of paper

Solution:  Since 2 pages can go on each sheet of paper, that means that the first 18 sheets of paper can fit on half of 18 = 9 sheets of paper. The 19^th page goes on a 10^th sheet of paper. So, 10 pieces of paper are needed for the whole reading assignment.

Upper Elementary:

Question: Sebastian completed 4 math assignments, 5 writing assignments, 7 reading assignments, 3 history assignments, and 1 science assignment last week. Fill in the pie chart to the right with Sebastian’s homework assignments.

Solution:  Answers vary, but the math assignments should take up 2 segments on the pie chart, writing should take 2½, reading should take 3½, history should take 1½, and science should take ½.

Middle School:

Question: Lisa needs to memorize the locations of all 54 countries in Africa for a geography test that will be 30 days from now. She memorizes 7 countries every 3 days. Every 2 days, she forgets a country and needs to re-memorize it. Will she have enough time to memorize all of the countries in Africa for her geography test?

Answer:  Yes

Solution:  Since there are 10 3-day periods in 30 days, Lisa can memorize the location of a country a total of 7 × 10 = 70 times. That means she has time to forget and relearn 70 – 54 = 16 of them. If she forgets 1 every 2 days, that means she forgets 30 ÷ 2 = 15 of them, and since 15 is less than 16, she will have time to re-memorize them all.

Algebra and Up:

Question: Logan has answered 0.8 times as many math questions as Spanish questions, and he’s answered 5 more English questions than Spanish questions. If Logan has answered 33 questions in total, how many math questions has Logan answered?

Answer:  8 math questions

Solution:  We can set up and solve the following system of equations to solve this problem:

M = 0.8S

E = S + 5

M + S + E = 33

Next, we plug the values of M and E into the third equation because they’re both already in terms of S. Now we have an equation with one variable—S. We can solve it to find that S = 10, so M must be 8. Logan has answered 8 math questions.

Challenge problem to take home. 20 points for the correct answer. 

Nora is playing a game in which she tries to guess whether an unknown binary number – which is five-digits at most - will be even or odd.

After making her guess, she will press a button. Then two of the five zeroes will randomly become ones, revealing the unknown number.

Should Nora guess even or odd?

Answer: Even