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For The Mathematically Inclined


Submitted by Aadhaarshila (ATFS)  The Math and Science Institute 10/10/2003
FOR CHILDREN
PROBLEM # 1
What rate of return is needed to earn $960 on an investment of $6840? PROBLEM # 2
A collection of quarters and dimes amounts to $4.35. If there are 33 coins coins in all, find the number of each coin.
FOR GROWNUPS
PROBLEM # 3
We have selected a secret fourdigit number. Your task is to determine this number. Column One contains guesses for the fourdigit number. A "D" in
Column Two indicates that the guess has one digit in common with the secret number. A "P" indicates that the guess has one digit in common with the secret
number and it is in the correct place. For example, if Column One Column was 1546 and Column Two showed D D, then two of the digits are correct but they are not in the correct place. If Column Two showed D P P, then three of the digits would be correct with two of them in the correct place.
Col. One Col. Two
3 9 2 0 . . D D D
8 7 4 5 . . P
9 0 7 5 . . D D
8 3 9 7 . . D D D
What is the secret number?
MATH SMART  Starting this issue of Lokvani, ATFS is introducing a Math Smart section for our readers. This section will provide a Smart trick for faster calculations.
MATH SMART TIP of the issue:
For Subtraction from numbers like 100, 1000, 1000, 10000 etc.. use the rule ALL FROM 9 LAST FROM 10. All numbers must be subtracted from 9 and the right most number from 10.
For example 1000  357 = 643
Try some yourself:
1) 1000  777 5) 10000  9876 9) 10,000  321
2) 1000  283 6) 10,000  1101 10) 10,000  38
3) 1000  505 7) 100  57
4) 10,000  2345 8) 1000  57

Please send your solutions to both problems to anil@lokvani.com.
Use "Problem Solutions M102303" as the subject line. Please include your full name in
the text of the main message. The first one to submit the right answer will be profiled in
the next issue of Lokvani.
Please do not post your solution in "Post Comments". No credit will be give for
solutions not sent to anil@lokvani.com.
If you need clarification on any problem, please contact anil@lokvani.com.
 SOLUTIONS TO PROBLEMS ON 10/09/03
PROBLEM # 1
Marty has exactly 5 blue pens, 6 black pens and 4 red pens in his knapsack. If he pulls out one pen at random, what is probability that the pen is either red or black?
SOLUTION
2/3. PROBLEM # 2
The average of 20, 70 and x is 40. If the average of 20, 70 , x and y is 50, then y is = ?
SOLUTION
80.
PROBLEM # 3
You own a factory that makes metal patio sets using two processes. The hours of
unskilled labor, machine time and skilled labor per patio set are given in the table below.
You can use up to 4000 hours of unskilled labor, up to 1500 hours of machine time and
up to 2300 hours of skilled labor. How many patio sets should you make by each process to
maximize profits, which is $80 for a patio made by Process A and $40 for a patio made by
Process B?
Assembly Hours  Process A  Process B 
Unskilled labor  10  1 
Machine Time  1  3 
Skilled Labor  5  2 
SOLUTION
300 by Process A, 400 by Process B.
P = 80a + 40 b
The constraints are as follows
10a + b < 4000
a = 3b < 1500
5a + 2b < 2300
a > 0
b > 0
The profit at each vertex of the graph is as follows.
At (0,500) : P = $20,000
At (300,400): P = $40,000
At (380,200): P = $38,400
At (400,0) : P = $32,000
At (0,0) : P = $0
Winners
Congratulations to S. Divatia, R. Doshi, S. Krishnakumar and B. Venkatraman, who were all winners of the last puzzle. (Note: The above tip has been adapted from Vedic Math. Please keep reading Lokvani issues for MATH SMART Tips.
ATFS is currently offering Saturday classes focused on Academic activities where among other things children of all ages learn these tips and tricks. Please call Gauri for details  508 845 0140 or write to us at gauri@atfsonline.com.
)

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