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 four-digit number. Your task is to determine this number. Column One contains guesses for the four-digit 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 M-102303" 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.

|