Problem of the Week October 2

Happy Back-to-School Season, Mathletes!

To celebrate the start of this 2017/2018 school year, we’re giving away a Mathnasium goody bag! To enter, all you need to do is scan a completed copy of any of September’s back-to-school themed Problem of the Week Extension Sheets and send it to [email protected] before October 6. The winner will be chosen at random. We will announce the winner with the October 9 set of Problems of the Week on Mathnasium Matters. Please limit entries to one per student and make sure all your extension sheets have your students’ names on them.

We wish you all the best of luck in the upcoming year!

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?
 

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.
 

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?
 

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?
 

WARNING: ANSWERS COMING 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 19th page goes on a 10th 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.