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Page 9

 

A Mixture Problem?

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Ms. Wong likes to mix grape juice with apple juice.  She calls the mixture grapple juice.   Ms. Wong starts with a pitcher containing 45 ounces of grapple juice that is 20 percent grape and 80 percent apple.  After tasting the mixture, Ms. Wong decides that it contains too much apple, so she adds 15 ounces of grape juice and mixes thoroughly.   For the teachers' lunch, she pours the juice from the contents of the whole pitcher into four large glasses, with the same portion in each glass.  Mr. Bender prefers grapple juice that is 25% grape and 75% apple.  How many ounces of apple juice must she add to her glass to make her juice taste the way she likes it?

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Answer: 9 ouncesThe pitcher starts with 9 ounces of grape juice and 36 ounces of apple juice, since 20 percent of 45 ounces is 9 and 80% of 45 ounces is 36.  Adding 15 ounces of rape juice gives a total of 60 ounce of grapple juice, in which 9+15 =24 ounces are grape and 36 ounces are apple.  By pouring the equivalent amount of grapple juice into 4 glasses, each glass will contain 24 4 = 6 ounces of grape and 36 4 = 9 ounces of apple juice.  Mr. Bender wants grapple juice that is 25% grape and currently has 6 ounces of grape in his glass;   therefore,  he needs a total of 18 ounces of apple in his glass,  since 6 is 25% of 24.  He needs a total of 24 ounces of grapple juice in his glass.  So she has to add 9 ounces of apple juice.

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What's the Change???

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Aaron has 100 coins, all of which are nickels, dimes, and quarters, that together are worth $13.  He has 3 times as many nickels as dimes.  How many of each type of coin does Aaron have?

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Answer: 48 nickles, 16 dimes, and 36 quarters.  If he has d dimes, then he must have 3d nickels and 100 - 4d quarters.  Solve the equation 5(3d + 10d + 25(100 -4d) = 1300 to find that d = 16.

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Your Summer JOB!

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Your new summer job is at the local swimming pool.  One hot summer day, 242 people are at the pool.  You notice that twice as many children as adult females are at the pool.  Also, 10 fewer adult men than adult females are at the pool.  Determine the number of children, female adults, and male adults that are at the pool.

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Answer: The numbers are 126 children, 63 adult women, and 53 adult men. A guess and revise method is shown in the chart below.  Alternatively, we notice that each time the number of children increases by 2,  the total number of people in the pool increases by 4.  To increase the number in the pool from 190 to 242,  we need to add (242 -190)/4 = 13 increments of 2 children , or 26 children , to the initial 100.  Finally, using a system of equations, if we let F equal the number of adult females , C equal the number of children , and M equal the number of adult males, we have the following:  F + C + M = 242... C = 2F.... M = F-10.  Substituting for C and M in the first equation, we get F + 2F +(F-10) = 242.  When we solve for F, we can find C and M. 

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The Long Walk

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Bradley and his younger cousin Gavin were hiking a 3.9-mile trail while on vacation in the Smoky Mountains.  Bradley's stride is 18 inches from the heel of one foot to the heel of the other.  Gavin's stride is 14 inches.  How many strides does Gavin make in 1 mile?  If Bradley walks at the rate of Gavin's stride per mile, how far ahead of Gavin will he be when Gavin completes 3.9  miles?

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Answer: Gavin makes 4526 strides in 1 mile.  When Gavin hikes 3.9 miles, if Bradley is walking stride for stride, Bradley wakls 5 miles, or 1.1 miles farther.  A mile equals 63,360 inches.  With a 14 inch stride, Gavin has to make 63360/14, or 4526, strides in a mile.  For Gavin, this number means 17,651 strides in 3.9 miles.  If Bradley makes the same number of stridesm, he has gone 18 x 17,651 inches, or 317,718 inches, which is about 5 miles.

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The Last Questions of '00 - '01

#1) To deliver Mail, the Canadian Post Office uses postal codes beginning with a letter and alternating 3 letters and 3 digits, such as H9W 2B3.  How many postal codes are possible with such a format?   Use the digits 0-9 and the letters A-Z except O, which can be confused with zero. (2pts)

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#2) Robin wants to ice a three-layer cake.  She uses a fruit filling between the layers, so she needs to cover only the visible parts of the cake.  Each layer is a cylinder that is 4 inches high.  The diameters of the bottom layer, middle layer, and top layer are 14 inches, 10 inches, and 6 inches, respectively.  What is the total area of the cakes surface on which Robin can put iciing?  Round your answer to the nearest square inch (let pie = 3.14). (3pts)

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#3 What day of the week begins a month that has a Friday the 13th? (1pt)

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#4) Despite being a reformed character, when Ebenezer Scrooged finally died he couldn't resist making hard for his relatives to get their hands on his wealth.  He hid the money and left them this note can you work out where the treasure lies hidden?  (3pts)

KXXL

RXDNX

XHT DLX

KXX XXRT

NX YM

NXDRXG

Extra, Extra Credit... Find the spelling & grammar mistakes (just here).

Answers:

#1) 15,625,000.  Multiply the number of possibilities for each entry to obtain 25 x 10 x 21 x 10 x 25 x 10 possible codes.

#2) 531 square inches.  If you "unroll" the lateral surface of each layer, you have a rectangle whose length is the circumference (i.e. pie times diameter) of the layer and whose height is 4 inches.  So the total area of the lateral surfaces is 14pie(4) + 10pie(4) + 6pie(4) = pie times 4 times (14 + 10 + 6) or about 377 sq. inches.  For the remaining circle an tow rings on the exposed tops of the layers, a helpful relationship to recognize is that these three surfaces combine to form a circle that is 14 inches in diameter.  Since the radius is 7 in, the circular area of icing is 49pie, or about 154sq inches.  You can also compute the "top" area by computing the area of the top of each layer and subtracting the area of the layer that rests on it.

#3) Sunday.  One week is 7 days, so the Friday before Friday the 13th must have been Friday the 6th.  therefore, the first of the month occurs six days before, or on a Sunday.

#4) "Look  under the old oak tree in my garden."  The words are written backwards and every vowel is replaced with an X.

Extra, Extra... you'll have to find it yorself.... hehehe

 

How Many House Numbers???

Dina has three brass house-number digits: 2,3, and 5.  How many distinct numbers can she form using one or more of the digits?

 

Answer: There are 15.  2,3,5,23,32,25,52,35,53,235,253,325,352,523,532.

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the Question Mark????

To make the following statement true, the question mark between the 6 and the 3 should be replaced by what operation?

(6?3) + 4 - (2 -1) = 5

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Answer: The Question mark should be a division sign.

 

the multiplication Pyramid

Write a number in each box below so that each number is the product of the two numbers beneath it.  Only whole numbers greater than 1 may be used.  In your answer use the letter to tell me the number and where it goes.

a)

294

b)

c)

21

d)

e)

f)

g)

5
 

Answer:  a) 92,610     b) 315   c) 14  d) 15   e) 2  f) 7  g) 3

 

The vote

Ninety-six ballots were cast in the seventh-grade presidential election.  Brett received twice as many votes as Stacy.  How many votes did each student receive? Explain how you know that your answer is correct.  (3pt)

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Answer:  Brett64; Stacy 32.  Because Brett received twice as many votes as Stacy,  if we divide the total number of votes by 3, we know that Bret received 64 votes or two-thirds of the total, and Stacy received 32 votes, or on-third of the total.

 

 

 

 

 
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