[last updated April 11, 1999]




week XIII/semana X1II: Mar 1  5 
week XIV/semana X1V: Mar 15  19 
Egyptian Obelisks: Ap 1 
week X /semana X: Jan 25  28 
week XI /semana XI: Feb 1  5 
week X11 /semana X1I: Feb 16  19 
week VII/ semana VII: Jan 4  8 
week VIII/ semana VIII: Jan. 1115 
week IX/ semana IX: Jan. 1822 
week IV/semana IV: Nov 1620 
week V/semana V: Nov.30  Dec 4 
week VI/semana VI: Dec 7  11 
week I/semana I: Oct 2630 
week II/semana II: Nov 26 
week III/semana III: Nov 913 
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Solutions to Week XIV:
Monday:
3 gallons = 1500 square feet3g = 1500
^{3}/_{3}g = ^{1500}/_{3}
g = 500 square feet
Tuesday:
1 gallon = 400 square feetg = 400
3g = ?
3 (400) = 1200 square feet
Wednesday:
GIVEN:g = 400 square feet
FIND:
Must cover 1500 square feet; how many gallons of paint must I buy?
Xg = ^{1500 }/_{400}
X = 3.75 gallons; therefore, I must buy 4 gallons of paint
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Solutions to Week XIII:
Monday:
Area = (Pi) (r^{2})
diameter = 7; r = ^{7}/_{2}
Pi = ^{22}/_{7} or 3.14
Area = ( ^{22}/_{7}) (^{7}/_{2})^{2} = ( ^{22}/_{7}) (^{7}/_{2}) (^{7}/_{2}) = (22) (7) ÷ (2) (2) = 38.5 square inches
Tuesday:
Area = (Pi) (r^{2})
diameter = 9; r = ^{9}/_{2}
Pi = ^{22}/_{7} or 3.14
Area = ( ^{22}/_{7}) (^{9}/_{2})^{2} = (^{22}/_{7}) (
^{9}/_{2}) (^{9}/_{2}) = (22) (81) ÷ (7) (2) (2)= 63.6 square inches
Wednesday:
Area = (Pi) (r^{2})
diameter = 11; r = ^{11}/_{2}
Pi = ^{22}/_{7} or 3.14
Area = ( ^{22}/_{7}) (^{11}/_{2})^{2} = (^{22}/_{7}) (^{11}/_{2}) (^{11}/_{2}) = (22) (121) ÷ (7) (2) (2)= 95 square inches
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Solutions to Week XII:
Tuesday:
Remember: OF usually translates to times in mathematics. Therefore,
^{1}/_{2} of ^{1}/_{6} is ( ^{1}/_{2} ) ( ^{1}/_{6}) = ^{1}/_{12} of the land is covered with pine trees
You might also find the solution by drawing a picture:
^{1}/_{2} ^{1}/_{6}
^{1}/_{12}^{1}/_{2} of land ^{1}/_{2} of land
Wednesday
16 ^{2}/_{3}  12 ^{1}/_{4 }=
make into an improper fraction
^{50}/_{3} ^{49}/_{4} =
find the common denominator
( ^{4}/_{4} ) ( ^{50}/_{3})  ( ^{3}/_{3} ) ( ^{49}/_{4}) =
make the equivalent fractions
^{200}/_{12} ^{147}/_{12} =
subtract
^{53}/_{12} =
make into a mixed number
4 ^{1}/_{12} tons of coal
Thursday
Remember: OF usually translates to times in mathematics. Therefore,
^{3}/_{4} of 316 balloons is( ^{3}/_{4} ) (316) = ^{(3) (316)}/_{4} = ^{948}/_{4} = 237 balloons are orange.
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Solutions to Week XI:
Monday:
given:
30 seconds ad costs $1.6 million
find:
How many minutes must be sold to make $1 billion dollars?
1 minute = (2) ($1,600,000) = $3,200,000
$1,000,000,000 = 312.5 minutes
$3,200,000 312.5 minutes ÷ 60 minutes = 5 hours 12.5 minutes
THEREFORE, the number of minutes required to sell and show $1 billion of Superbowl ads would take more time than the entire superbowl broadcast lasted, even if they skipped showing the game all together and just showed the ads.
Mr. Sovel was right, but Mrs. Sovel won the bet [dessert at her favorite restaurant on Valentines Day].
Tuesday
state the problem:
(2 ^{1}/_{2}) pounds  (^{3}/_{8}) pounds =
change all mixed numbers to improper fractions:
(^{5}/_{2})  (^{3}/_{8}) =
find the least common denominator:
(^{4}/_{4}) (^{5}/_{2})  (^{3}/_{8}) =
subtract the numerators:
(^{20}/_{8})  (^{3}/_{8}) = (^{20  3}/_{8}) = (^{17}/_{8})
make a mixed number again:
(2 ^{1}/_{8}) pounds
Wednesday
state the problem:
(^{1}/_{2}) cup + (1 ^{1}/_{3}) cup + (^{1}/_{4}) cup =
change all mixed numbers to improper fractions:
(^{1}/_{2}) cup + (^{4}/_{3}) cup + (^{1}/_{4}) cup =
find the least common denominator:
(^{6}/_{6}) (^{1}/_{2}) + (^{4}/_{4}) (^{4}/_{3}) + (^{3}/_{3}) (^{1}/_{4}) =
add the numerators:
(^{6}/_{12}) +(^{16}/_{12}) + (^{3}/_{12}) =
(^{6 + 16 + 3}/_{12}) = (^{25}/_{12})
make a mixed number again:
(2 ^{1}/_{12}) cups
Thursday
state the problem:
(2 ^{2}/_{3}) kiloliters (12) months =
change all mixed numbers to improper fractions:
(^{8}/_{3}) (^{12}/_{1}) =
multiply
(^{(8) (12)}/_{(3) (1)}) = (^{96}/_{3})
make a mixed number again:
32 kiloliters per year
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Solutions to Week X:
Monday:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610explanation: a number is the sum of the prior two numbers, that is, the two numbers that come before it.
Tuesday
200 miles divided by 13 miles per gallon200 miles ÷ 13 ^{miles}/_{gallon} = (200) (
miles) (^{1}/_{13}) ( ^{gallons}/_{miles}) =15.38 gallons = 15 gallons for the jeep
Wednesday
200 miles divided by ^{3}/_{5} miles per gallon200 miles ÷ ^{3}/_{5} ^{miles}/_{gallon} = (200) (
miles) (^{5}/_{3}) ( ^{gallons}/_{miles}) =^{ }^{1000}/_{3} gallons = 333.33 gallons =
333 gallons for the tank
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Solutions to Week IX:
Tuesday:
Two approaches:First approach:
find the prime factors of each of the numbers:
4 = (2) (2)15 = (3) (5)
The number that will be divisible [that is, a factor of] into all numbers divisible by both 4 and 15 will either have the factors (2)(3) = 6 OR (2)(5) = 10. Therefore, the numbers 6 and 10 will be such factors. As the list only includes 6, that is the answer.
Second approach:
Set up a table to test several numbers that are divisible by both 4 and 15, then test the various choices;
60 120 180 6
yes yes yes 8
no yes no 18
no no yes 24
no no no 45
no no yes 6 is the only solution offered that is a yes each time, therefore 6 is the answer.
Wednesday:
(^{1}/_{2})(^{1}/_{2}) ÷ (^{1}/_{2}) = (^{1}/_{4}) ÷ (^{1}/_{2}) = (^{1}/_{4}) (^{2}/_{1}) = (^{2}/_{4}) = (^{1}/_{2})
Thursday
The best choice is the one that starts at 1 cent the first day: The total sum earned
would be $10,737,418.23 earned over a 30 day period.
Days 
Amount per day

1 
$0.01

2 
$0.02

3 
$0.04

4 
$0.08

5 
$0.16

6 
$0.32

7 
$0.64

8 
$1.28

9 
$2.56

10 
$5.12

11 
$10.24

12 
$20.48

13 
$40.96

14 
$81.92

15 
$163.84

16 
$327.68

17 
$655.36

18 
$1,310.72

19 
$2,621.44

20 
$5,242.88

21 
$10,485.76

22 
$20,971.52

23 
$41,943.04

24 
$83,886.08

25 
$167,772.16

26 
$335,544.32

27 
$671,088.64

28 
$1,342,177.28

29 
$2,684,354.56

30 
$5,368,709.12

total 
$10,737,418.23

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Solutions to Week VIII:
Monday:
This is an example of using dimensional analysis to move from one set of units of measurement to another:
(60 ^{sec}/ _{min})(60 min/^{ } _{hour})(24 hours/^{ }_{day}) = 86,400 ^{sec}/^{ }_{day}
1,000,000,000
seconds= 11,574 days
86,400
^{seconds}/^{ }_{day}
Tuesday
It may be helpful to number the ribbons 1, 2, 3, 4, 5, and 6. Ribbon 1 can be worn with ribbons 2, 3, 4, 5, and 6, giving 5 combinations. Ribbon 2 can be worn with ribbons 3, 4, 5, and 6, giving 4 more combinations. (You would not recount ribbon 2 with ribbon 1, since that was counted in the first step.) Similarly, ribbon 3 can be worn with ribbons 4, 5, and 6, ribbon 4 can be worn with ribbons 5 and 6, and ribbon 5 can be worn with ribbon 6. The total number of combinations is 5 + 4 + 3 + 2 + 1 = 15 combinations.
Thursday
Each man will play 1 game of chess with each of the 5 women. Therefore, each man will play 5 games. Since there are 5 men, there is a total of 25 games played between the men and the women. Each woman will play one game of chess with each of 4 other women. In counting the number of games played, it is important to avoid counting any game more than once. The first woman will play 4 games. The second woman has already played the first woman, so she will play 3 additional games with the other women. Similarly, there are 2 more games played by the third woman, and one more game played by the fourth woman. The games played by the fifth woman have already been counted. So, 5 women play a total of 4 + 3 + 2 + 1, or 10 games. Thus, a total of 35 games of chess have been played
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Solutions to Week VII:
Monday:
Two simple approaches might be used.The first is a ratio:
6 lemons = X 2 quarts 8 quarts
(6 lemons) (8 quarts)= X = 48 lemons = 24 lemons
2 quarts2 The second approach simply finds out how many lemons are needed to make 1 quart [by dividing 2 into both 6 lemons and 2 quarts], then multiplying the result by 8 quarts.
(3) (8) = 24 lemons
Tuesday
This solution/strategy has the following assumptions:












subtotal: 




Wednesday
step 1: subtract ^{2}/_{3} from 1, in order to find the volume still to be filled. [ ^{1}/_{3} ]step 2: to find ^{1}/_{3} of 15 gallons, multiply the two terms = 5 gallons
Thursday
It takes 10 minutes for one pizza maker to make one pizza.
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Solutions to Week VI:
Monday:
A number of solutions approaches may be used
 create an XY graph, with the Xaxis being the distance from shore and the Yaxis being the depth.
 draw a picture
 divide the depth by 1.5
9 meters divided by 1.5 meters = 6 meters
Tuesday:
First find out how many 15 minute increments there are in two hours:
 2 hours times 60 minutes per hour = 120 minutes
 120 minutes divided by 15 minutes = 8
Then multiply 1.5 kilowatts [per 15 minutes] times 8 [the number of 15 minute groupings] = 12 kilowatts
Wednesday
What do we know?
 1 dozen = 12
 regular price is 39¢ each or (12) (39¢) = $4.68 per dozen
 special price is 3 for 89¢ or (4) (89¢) = $3.56 per dozen
Find the difference [subtract] = $1.12 savings per dozen, at the special price
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Solutions to Week V:
Monday
(10 feet)(12 inches per foot) = 120 inches divided by 37 inches per shelf = 3 shelves, with 9 inches of waste, per 10 foot board.If 15 shelves are needed, divide 15 by 3 [per 10 foot board] = 5 boards needed to make the shelves.
Tuesday
Method 1:
Add up all the weights in frames #1, #2, and #3 = 25.2 kilos. This accounts for all three sizes of chickens, twice each. Then divide this total by 2 =frame #4: 12.6 kilos.Method 2:
Add frames #1 and #2 =19.1 kilos. Subtract frame #3 [19.1  6.1] = 13 kilo or the weight of the two large chickens. Therefore one large chicken weighs 6.5 kilo. Add this to frame #3 for a total of 12.6 kilos.
Wednesday
First find the unknown height [6cm + 9cm =15 cm], then find the unknown length [18 cm + 11 cm = 29 cm]. Now add all the lengths and heights, as if you decided to walk all around the figure = 88cm.
Thursday
Using the information from finding the dimensions of the unknown sides from Wednesday's problem, you may form several different combinations of rectangles. For example, one pair may be [18 cm x 15 cm] + [11 cm x 9 cm] = 369 square centimeters.
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Solutions to Week IV:
Monday:
up $2.50
+ 2.50up $3.00
+ 3.00down $1.25
 1.25 gain of $4.25original cost:
$30.50current price:
$34.75
Tuesday
total burn [in seconds]
1145.01st stage burn
 86.8second stage burn [in seconds]:
1058.2
Wednesday
2 people for 4 months [$645/2 = $322.50]3 people for 8 months [$645/3 = $215.00]
4(322.5) + 8(215) = 3010
January
$322.50
February
$322.50
March
$322.50
April
$322.50
May
$215.00
June
$215.00
July
$215.00
August
$215.00
September
$215.00
October
$215.00
November
$215.00
December
$215.00
Merry's cost for
one year$3,010.00
Thursday
Angler's price
$69.95less discount
 $10.49Go Fish Discount price:
$59.46
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Solutions to Week III:
Tuesday:
Divide the day pass price by the single ticket price:$14.00 ÷ $3.75 = 3.73, therefore four or more single rides would be less expensive with a day pass.
Thursday:
Note: The question asks about lunches over a 4 week period, therefore:(2) ($20) = $40.00 in allowance
$7.50 + $8.25 + $ 5.25 + $ 8.75 = $29.75 spent
Find the difference: $40.00  $29.75 = $10.25 left over.
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Solutions to Week II:
Monday:
(July ÷2) + (August) = total spent($75.80/2) + ($75.80) = $37.90 + $75.80 = $113.70
Tuesday:
(Monday) + (Tuesday) + 2(Monday + Tuesday) = total boxes moved(453) + (485) (453 + 485) = 453 + 485 + 938 = 1876 boxes moved
Wednesday:
If the dimensions increased 4 times, to find the original dimensions, you must dived by 4:19.2 cm /4 = 4.8 cm
25.6 cm /4 = 6.4 cm
Thursday:
Divide the total number of passengers by the total number of buses:392 / 8 = 49 passengers per bus
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Solutions to Week I:
Monday:
note: make all the amounts the same units, therefore:16 oz.(1 pound) + 12 oz. + 6 =
16 + 12 + 6 = 34 ounces or 2 pounds 2 ounces
Tuesday:
Add the perimeters of each windownote: when adding, be sure to line up the decimals
4.85 m
4.25 m
2.55 m11.65 m
Wednesday:
Find the total spent, then divide by the number of people:$41.50 + $6.15 = $47.65
$47.65 ÷ 3 = $18.883
Therefore, 2 people paid $18.88 each and one person paid $18.89
Thursday:
Find the cost of the computers in one classroom, then multiply for all the classrooms:(4) ($865) = $3,460
(12) ($3,460) = $41,520 total
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