Algebra 1 – Problems of the week

POW Answer Sheet

Due September 6- 9

Suppose you need to measure exactly 1 cup of water.
All that you have in your kitchen are two containers.
The smaller container holds 3 cups and the larger holds 5 cups.
How can you use these two containers to measure exactly 1 cup of water?

Due September 12-16

While flying over farmland, a pilot notices the rectangular shape of the fields below.
She sketches the lines that divide the fields. When she returns to the airport,
she wonders how many different rectangles can be formed by the lines drawn?
HINT: Don’t forget that a square is also a rectangle.

Due September 19-23

What is the largest three-digit number that is a multiple of 13?

Due September 26-30

To move their armies, the Romans built over 50,000 miles of roads. Imagine driving all those miles!
Now imagine driving those miles in the first gasoline-driven car that has only three wheels and
could reach a top speed of about 10 miles per hour.
For safety’s sake, let’s bring along a spare tire.
As you drive the 50,000 miles, you rotate the spare with the other tires so that all four tires
get the same amount of wear.
Can you figure out how many miles of wear each tire accumulates?

Due October 3- 6

One of the following four-digit numbers is not divisible by 4: 3544, 3554, 3564, 3572, 3576.
What is the product of the units digit and the tens digit of that number?

Due October 11-14

The Math Club is preparing for their first competition.
The entrance rules of the competition call for teams of three, where each team
must include at least one girl and one boy. No student can be on more than one team.
Of the 44 members that will be able to attend the competition, there are
eighteen more girls than boys.
What is the maximum number of teams the club can enter in the competition?

Due October 17-21

Chuck is buying some cola for his friends. He can go to the vending machine and
get 12 oz. cans for $.60 per can,
he can go to the corner store and get 20 oz. bottles for $.95 per bottle,
or he can go to the grocery store and get 32 oz. jugs for $1.45 per jug.
He has $4.25 to spend.
At which venue can he get the most cola? Is this the best buy?

Due October 24-28

Use each of the digits 3, 4, 6, 8, and 9 exactly once to create the greatest
possible five digit multiple of 6. What is that multiple of 6?t

Due October 31-Nov 4

Ann and Sue bought identical boxes of stationery. Ann used hers to write 1-sheet letters,
and Sue used hers to write 3-sheet letters. Ann used all the envelopes and had 50 sheets
of paper left, while Sue used all of the sheets of paper and had 50 envelopes left.
How many sheets of paper and how many envelopes were in the box to begin with?

Due November 7 – 11

Three big ducks went out one day
With two ducklings behind.
Fourteen kilograms was their weight
When all five were combined.

Add one duck and one duckling
And their weight increased.
Nineteen kilograms was the total
Of the seven with webbed feet.

If all ducklings have one weight,
and ducks all have another,
Then you should find the total weight
of three – one child, two mothers.

Due November 14-18

Using only 2, 3, 4, 5, “+” and “=”, and using each only one time, create a true equation?
2+3=45. uses all the signs and numbers but it is not a true equation.
You may not use any other signs or numbers.

Due November 21-22

A multiple of eleven I be,
Not odd, but even, you see.
My digits a pair,
When multiplied there,
Make a cube and a
Square out of me.
Who am I?

Due November 28-Dec 2

The mean, median, and mode are all equal for the set {3, 4, 5, 8, X}. What is the value of X?
Describe how you got your answer.

Due December 5 – 9

By using the answers to the following questions, Patrick determines Sam’s secret whole number.
Is it a factor of 30? Yes
Is it a prime number? No
Is it a multiple of 3? No
Is it less than 3? No
What is Sam’s secret number?

Due December 12 -16

Jo and Schmoe spent $207 on a shopping spree. One item they purchased cost $1.
All other prices were prime numbers (dollars only) and each digit (1 through 9) was used once and only once.
The digits of one item totaled 7. What was the value of each item?

Due December 19-22

The phone company has 25 computer-controlled switching systems.
Each system handles 700,000 calls an hour. Each system works correctly 95% of the time.
How many calls WOULD NOT BE CORRECTLY handled in one 24 hour period assuming
each of the 25 systems was running at maximum capacity at all times?

Due January 3 – 6

Write any 3 digit number (xyz where x, y, and z are digits) and then repeat it so you have a
6 digit number (xyz,xyz). Divide the 6 digit number by 7.
Divide that answer by 11. Divide that answer by 13.
Your answer after the 3 divisions will be xyz, even if you divide by 7, 11, and 13
in a different order. Why does that work?

Due January 9 – 13

A company assesses shipping charges of $3 for the first item in a package,
$2 for the second item, and $1 for each additional item.
For example, the charge for one package of four items is $3 + $2 + $1 + $1 = $7.
How much is saved by shipping ten items in two packages of five items each,
rather than in five packages of two items each?

Due January 17 – 20

Inside a large box are six smaller boxes. Some of these smaller boxes are
empty, and others have six very small empty boxes inside them. Thirty-one
boxes in all are present. How many of these 31 boxes are empty?

Due January 23 -27

Jessica has an odd number of stamps in her collection. The sum of the
digits in the number of stamps she has is 12. The hundreds digit is three
times the ones digit. If she has between 1000 and 2000 stamps in her
collection, how many stamps does Jessica have?

Due January 30 – Feb 3

A student needs at least a 65 pass Algebra 1. During the
first two quarters the student averaged 50. What is the minimum the student
must average during the last two quarters to pass for the year?

Due February 6 – February 10

A cage at the Milwaukee County Zoo contains both peacocks and wild pigs.
If a total of 30 eyes and 44 feet are counted, how many peacocks are in the

Due February 13-17

Holton has 19 toothpicks. How many ways can he arrange them into three
piles so that each pile contains an odd number of toothpicks?

Due February 27-Mar 2

One zip weighs as much as three zaps. Two zaps weigh as much as five
zowies. Three zowies weigh as much as two swooshes. If one swoosh wieghs
sixty pounds, how manay pounds does one zip weigh?

Due March 5 – March 9

Five candidates A, B, C, D, and E were in an election. Candidate A won
with 30 votes, B placed second, and E placed last with 3 votes. If 49 votes
were cast, and no two candidates had the same number of votes, what is the
smallest number of votes that B could have received?

Due March 12 -16

A ball is dropped 128 feet from the roof of a building. Suppose that with
each bounce, the ball goes up exactly half its previous height. A man is
sitting at his desk on the second floor. How many times will he see the ball
if his eye level is 15 feet above the ground?

Due March 19 -22

An electrical panel has 100 switches in a row, all in the off position.
Every second switch is turned on and then every third switch is changed from
whatever posittion it is in to the other position. How many switched are now
in the on position?

Due March 26-30

The mean of a list of 7 numbers is 45. If I add 2 numbers to the list,
the mean of the list becomes 37. What is the mean of the two numbers that I
added to the list?

Due April 2 -6

Using each of the digits only once, in how many ways can the digits 2, 4, and 6 be placed,
one digit per box, such that:

Due April 9 – 13

What are the last two digits of 6^999?

Due April 23 – 26

Calvin is 150 cm tall, which is 75 percent of Darryl’s height.
How many centimeters tall is Darryl?

Due April 30 – May 4

To make a pen for his new pony, Ted will use one side of the barn
and ninety-six feet of fencing. What are the dimensions of the
rectangular pen that he can make that will have the greatest area?

Due May 7 – 11

A certain kind of folder was priced at 50 cents but found no buyers.
The manager of the store decided to reduce the price. Within a few days,
she sold her entire stock for $31.93.
What was the reduced price of the folder?

Due May 14 – 18

Toss a pair of dice and multiply the number of dots shown on the uppermost faces.
What is the probability of getting a product that is a multiple of 3?
A multiple of 5? A multiple of 3 or 5? A multiple of 3 and 5?
Hint: list all the possibilities you can get when you throw the dice.

Due May 21 – 25

A family has three daughters. The product of the daughter’s ages is 200.
The oldest daughter is twice the age of the middle daughter.
How old is each daughter?

Due May 29 – Jun 1

Zach gets a commission on items he sells at a men’s store.
He gets $4 for a jacket, $3 for a pair of pants, and $1 for each shirt,
but receives no commission for ties or socks.
Today, Zach sold 7 items and earned $20 in commissions.
List all possible sets of items he could have sold.

Due June 4 – 8

1Stacy sets her clothes out before going to bed so that she does not have to turn on

her light in the morning. One morning, she realizes that she forgot to set out a pair of blue socks.
If her drawer contains 11 blue socks, 9 black socks, and 10 brown socks,
how many socks must she remove from the drawer to guarantee that she has a blue pair?

Most problems copyright © 2001-5 National Council of Teachers of Mathematics.