Answers to Problems of the Week - July 5 to July 11

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: George plans to read all of Chapter 4 in the book he’s reading tonight. Chapter 4 starts on page 75 and ends on page 100. How many pages does George plan to read tonight?

Answer:  26 pages

Solution:  First, we find how far apart page 100 is from page 75: 100 – 75 = 25. Next, we need to add 1 page because find­ing the difference counts page 100 but not page 75. So, 25 + 1 = 26 pag­es.

Upper Elementary: 

Question: Yesterday, Max read half of a book. Today, he read a third of what was left. What fractional part of the whole book is left for Max to read?

Answer:  One Third

Solution:  After Max reads half of the book, there’s one half left. A third of a half is a sixth, so Max has read 1/2 +1/6 = 3/6 + 1/6 = 4/6 = 2/3 of the book. That means he has 1 - 2/3 = 3/3 - 2/3 = 1/3 of the book left to read.

Middle School: 

Question: Amelia can read 150 words per minute. The book she’s reading is 450 pages long and has 250 words on each page. How many hours will it take Amelia to read the whole book?

Answer:  12

Solution:  Amelia reads at a rate of 150 words/minute x 1page/250 words = 150 pages/250 minutes. We could reduce this rate further, but since 450 pages is a multiple of 150 pages, it’s easier not to. To read 450 pages, she needs to read 150 pages, 3 times. This means she reads for 250 minutes, 3 times, or 750 minutes. To find out how many hours that is we divide: 750 ÷ 60 = 12 1/2 hours.

Algebra and Up: 

Question: There are 3 books in a series. Altogether, the series is 1,155 pages long. Book 1 is the shortest—16 pages shorter than Book 3. Book 2 is 1 page longer than Book 3. How many pages long is each book?

Answer:  Book 1 is 374 pages, Book 2 is 391 pages, and Book 3 is 390 pages.

Solution:  Let’s call the books A, B, and C. We can create a series of equations:

A + B + C = 1,155

A = C – 16

B = C + 1

One way to solve this problem is to sub­stitute (C – 16) and (C + 1) into the origi­nal equation in the place of A and B. This leaves us with:

C – 16 + C + 1 + C = 1,155

Based on that equation, C = 390. If C = 390, then A = 374 and B = 391.

Challenge problem to take home. 10 stars for the correct answer. 

The City of Trees offers an Awesome Pass, which offers discounted access to many attractions. In the basic package, you need to pick one of two bus tours, one of four museums, and one of two palaces. However, if you opt for the Historic bus tour, you have to skip palaces but will visit two museums instead of one. Also, if you choose the Museum of Brilliance, the only palace you could visit is the Palace of Magnificence (if you haven't chosen the Historic bus tour). Assuming the order of attractions doesn't matter, in how many ways can you spend your weekend in the City of Trees?

Answer: 13 ways