# Problem of the Week 01-23-2017

Jan 24, 2017 | Coral Springs

Lower Elementary:

Question:  James trades a bottle cap for two thumb tacks. He trades each thumb tack for two paper clips. He trades each paper clip for two thimbles. Then, he trades each thimble for two bottle caps. How many more bottle caps does James have now than he did when he started?

Solution:   James trades the 2 thumb tacks for 2 doubled = 4 paper clips. He trades the 4 paper clips for 4 doubled = 8 thimbles. He trades the 8 thimbles for 8 doubled = 16 bottle caps. Sixteen bottle caps is 16 – 1 = 15 more bottle caps than he had when he started.

Upper Elementary:

Question:  A truck that itself weighs four tons carries one ton of gravel. The driver unloads 500 pounds of gravel at a construction site. How many pounds do the truck and the gravel weigh in total now?

Solution:   A ton is 2,000 pounds, so the truck itself weighs 2,000 × 4 = 8,000 pounds. After the truck leaves the construction site, it has 2,000 – 500 = 1,500 pounds of gravel in the back. In total, that’s 8,000 + 1,500 = 9,500 pounds.

Middle School:

Question:  One red token is worth the same as two blue tokens. One blue token is worth the same as five orange tokens. One red token is worth the same as five pink tokens. How many orange tokens are worth the same as a pink token?

Solution:   To solve this problem, we can think of a red token as “one whole.” If a red token is a whole, then each blue token is a half. If each blue token is a half, then each orange token is a fifth of a half, or tenth. A pink token is a fifth of a red token, so a fifth of the whole. It takes two tenths to make one fifth, so two orange tokens are worth the same as a pink token.

Algebra and Up:

Question:  Puppies sleep an average of 12 hours each day. Kittens sleep an average of 20 hours each day. If a puppy is 4 weeks older than a newborn kitten, then how old will the kitten be when the kitten and the puppy have gotten the same amount of sleep in total?

Answer:  42 days or 6 weeks.

Solution:   There are 28 days in 4 weeks, so the puppy has gotten 12 × 28 = 336 hours of sleep by the time the kitten is born. We want to know when the amount of sleep is equal. The kitten sleeps at a rate of 20 hours per day, and the puppy sleeps 12 per day with a 336-hour lead. We can set up the following equation and solve for d days:

20d = 12d + 336

d = 42

The kitten will be 42 days—or 6 weeks—old.