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POLYA’S FOUR-STEP PROBLEM SOLVING STRATEGY 1. Problem: There are 364 first year students in the Institute of Mathematics. If there are 26 more females than males, how many females are there? UNDERSTAND THE PROBLEM - Assuming every student is either a boy or a girl. We need to determine and examine if in 364 first year with 26 more females than males, we need to get the remaining numbers of female students. DEVISE A PLAN - Supposedly, in a 364 first year students with 26 more females, | will use basic mathematics and provide a situation related to the problem. CARRY OUT THE PLAN - Suppose all the first year students are in gymnasium. - Suppose 26 females leave the gymnasium to buy a snacks. Then there will be the same number of females as males. - There will be 364 — 26 or 338 students left in the gymnasium when the 26 females leave. - The males and the females left are half with the same numbers which is 169 males and 169 females. - The 26 remaining females came back and was added with 169 other females, there will be 169 + 26 or 195 females. REVIEWING THE SOLUTION - Because there are 364 students with 26 more females, Therefore, 169 + 26 female is equal to 195 females. - Checking: 195 females + 169 males = 364 students. 3.ln how many ways can you answer a 5 question true-false test if you can answer each question with either “true” or “false”? UNDERSTAND THE PROBLEM - In problem number 3, we need to identify if how many ways we can answer a 5- question true-false test if we can answer each item with either “true” or “false”. DEVISE A PLAN - After reading the problem, we will prepare and formulate a list of possible orders. We will use this method to answer the task because we already saw this technic on the recorded lecture discussion of Ms. Rifion. It’s more convenient and more comfortable for us to do and we viewed this method as the possible way in order for us to figure out the answer. After recording the all orders, we will sum it up and the total number it will be the answer for the question number 3. CARRY OUT THE PLAN 1. BRIT Tt. 13. TT TF IP. 25: TRIP T F 2 TIFF, 14.F FFTT. 26.FTTFT 3. TTFFT. 15.1 FTF T- 27.FTFTT 4. FFTTF. 16.F TFTF. 28.TFTFF 5. TFFTT. iF iTER. 29.F FTFT 6. FTTFF. 1S. TTFTT. 30. TTFTT 7. TFTTT 19.FTTTF. ah Tri 8. FTFFF. 20). THEFT. 32. FF FFF 9. TTTET: Z10F FRET 10.F FF TF. 22.TT TTF W1.FTFEFT. 23.TF FFE 12.7 TT F. 24.FTTTT - There are 32 ways to answer a 5-question true-false test if we'll answer each item with either “true” or “false”. CHECK THE SOLUTION - Definitely, We all agreed in our group that “32” is the final and also the correct answer in question number 3. Since it was mentioned in the problem that there will be a five question (1-5) true-false test and each of those items are can be answered with either “true” or “false”. So we recorded and assumed all the possible orders. And with that we came up with the total answer of ’32 ways’ which can be also interpreted as (2*5=32 or 2X2X2X2xX2=32) So yes, we are sure that in a 5-question true or false test it can be answered with either TRUE or FALSE in 32 different ways. 6. Mang Tomas owns goats and ducks. Counting heads there are 39. Counting the legs there are 110. How many goats and how many ducks Mang tomas have? UNDERSTAND THE PROBLEM - We need to find the exact number of all the goats and ducks Mang Tomas have. With the help of the given data that when you count the total ducks and goats by heads there are 39 in total while if you count them by legs there are 110 in total. DEVISE A PLAN - We've clearly seen that if we go higher than 23 & 16, we would end up with a number higher than 110. As well as, if we go lower than 23&16 we would end up with a number that is lower than 110. - Another important note, it’s 23 ducks & 16 goats, we can’t reciprocate them. It can’t be 23 goats and 16 ducks, for we would end up with a number higher than 110. So certainly and absolutely, Mang Tomas have a total of 23 ducks and 16 goats, that when we count by heads is 39 while 110 if we count by legs. 8. | am thinking of a two-digit number = Itis odd + It’s ten digit is even + It is prime * The sum of its digit is 11 * The product of its digit is 24 What number am | thinking of? UNDERSTAND THE PROBLEM - Weare given five (5) clues to find the unknown number. Thus, we need to perform certain step to satisfy all these given clues or conditions so we can the figure out the unknown. DEVISE A PLAN - First we need to read and understand the clues or conditions. It says that this unknown N is an odd, a prime, its ten digit is even, and when you add its digit the sum is 11 while when you multiply its digit the product is 24. Accordingly, the first step is to list all the prime numbers from 1-99. So, from our previous studies we've learned that prime number is those numbers that have no other factors except 1 and its number itself. After we list all the prime numbers, we can now proceed to other conditions. CARRY OUT THE PLAN 1. One condition stated that its ' tens’ is even, so we're just going to list all the prime numbers between 1-99. 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 59, 61, 67, 71, 78, 79, 83, 89, 97 Note: Obviously, the unknown is two digit number so we didn’t include in the list those 1 digit prime numbers 2. Let's now pick all the prime numbers that has even tens but an odd numbers 23, 41, 43, 47, 61, 67, 83, 97 3. Now we're going to add those numbers above and find that number who's digit has the sum of 11 24+3= 5 44125 443=7 4. Because we are left with just two numbers whose digit has the sum of 11, then now, we will multiply the digit of these two remaining numbers. And find the one who has the product of 24. 7x4= 28 8x3 = 24 Thus, 83 is our unknown number. REVIEW THE SOLUTION - There is no doubt that the unknown number is 83 because it’s the only number that satisfied all five given conditions. 83 is an odd number 1 It is prime 0 It's tens digit is 8 which is even “| 8 + 3 produce a sum of 11 | 8x3 produce product of 24 1) Certainly, 83 is the number you are thinking of. 7. Keith bought five pencils and pen at a total cost of Php.29. A pencil costs Php.4 and a pen costs Php.7. How many pen did Keith buy? UNDERSTAND THE PROBLEM - According to the given data, Keith bought five pencils & pens with a total costs of 29. Each pencil cost php.4 and each pen cost 7. As we can observed, we dan’t know haw many pens and pencils did Keith bought, and that's what we're going to find. DEVISE A PLAN 
