Problem Set B Solutions

Brown Bag PS Solutions – Set B
#1 Marcella’s Bagels
Marcella is carrying a bag of bagels on her way home.
Various people stop her three times along the way, each time taking
half of her bagels plus two more from her bag.
By the time she gets home, she has only two bagels left!
Sonya gets a trip to the park if she can determine how many bagels
Marcella had to start with.
Show your work using words, numbers, and/or pictures.
Solution
44 bagels
#2 It’s All Gone
A man goes into a store and says,“If you give me as much money
as I have with me now, I will spend $10 in your store.” The proprietor
agrees, and the man spends the money.
He goes into a second store and again says,“If you give me as much
money as I have with me now, I will spend $10 in your store.” Again,
the proprietor agrees, and the man spends the money.
In a third store, he repeats his proposition, the proprietor agrees, and
the man spends the money.
At this point, the man has no money left.
How much money did this man have to begin with?
Explain your answer. Show your work using words, numbers, and/or pictures.
Solution
$8.75
Solve for x: 2(2(2x-10)-10)-10 =0
Brown Bag PS Solutions – Set B
Problem of the Week
#3 Broken Eggs
A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over all the containers of eggs. Though she is
unhurt, every egg is broken. So she goes to her insurance agent, who
asks her how many eggs she had. She says she doesn’t know, but she
remembers some things from various ways she tried packing the eggs.
#4
When she put the eggs in groups of two, three, four, five, and six there
was one egg left over, but when she put them in groups of seven they
ended up in complete groups with no eggs left over.
What can the farmer figure from this information about the number of eggs she had? Show
your work using words, numbers, and/or pictures.
Solution
721 or any multiple of this number.
#4 The Number Magician
A magician said to a volunteer from the audience,
“Pick a number, but don’t tell me what it is.
Add 15 to it.
Multiply your answer by 3.
Subtract 9.
Divide by 3.
Subtract 8.
Now tell me your answer.” “Thirty-two,” replied the volunteer. Then the
magician immediately guessed the number that the volunteer had originally chosen.
What was the volunteer’s number? How did the magician know so
quickly? (The magician couldn’t possibly have worked backwards that
fast.) Show your work using words, numbers, and/or pictures.
Solution
36 Adds 4 to the volunteer’s number.
Brown Bag PS Solutions – Set B
#5 A Fractional Life
Here is a problem that is part of The Greek Anthology, a group of
problems collected by ancient Greek mathematicians.
Demochares has lived a fourth of his life as a boy, a fifth as a youth, a
third as a man, and has spent 13 years in his dotage. How old is he?
How old is Demochares?
(Note: The phrase “in his dotage” refers to the period of Demochares’
old age.)
Show your work using words, numbers, and/or pictures.
Solution
60 years old
1/4 = boy
1/5 = youth
1/3 = man
Find LCD = 60
Boy = 1/4 = 15/60 = 15 years
Youth = 1/5 = 12/60 = 12 years
Man = 1/3 = 20/60 = 20 years
15 + 12 + 20 = 47 years, and 13 years in his dotage, so he is 60 years old