Math Word Problem #1 - Questions and Answers

Question 1 Explain: In your own words, describe a step-by-step approach for solving algebraic word problems. Answer Word Problem: A word problem is a math issue that has been expressed as a narrative or scenario. It basically asks you to picture how you would use arithmetic to solve a real-world situation. Any word issue may be solved using the following method: Determine the issue's focus by carefully reading the problem. Use variables to represent unknown numbers. Convert the remaining portions of the issue to mathematical expressions. Resolve the issue. Verify your work. Example: Johnny, for instance, has 12 apples. How many will he still have if he gives Susie four? We can tell Johnny begins out with 12 apples from reading the issue that he ends up with 4 less since he gave some of them away. So, this may be written as: 12 − 4 = 8 So Johnny has 8 apples left. Question 2 Sofia's 4th grade class has a spelling list organized by subject. The spelling list includes 170 words about history, 75 words about science, 60 words about math, and 55 words about geography. Each week, Sofia's teacher tests her on 15 words from the list. Sofia's class has already had 7 weeks of spelling tests. How many more words will Sofia be tested on before the end of the year? Answer Solution: Total words are 170 + 75 + 60 + 55 = 360. Each week, Sofia is tested with 15 words from the list. Total number of weeks it will take to finish the list is 24. Average number of weeks in a year is 25 approximately. Seven weeks are already over, that means 15 × 7 = 105 15×7=105 words are covered from the list. Conclusion: Remaining words are 360 − 105 = 255 360−105=255. These words can be covered in a group of 15 in a week, so 255 15 = 17 15 255 ​ =17 are the number of weeks. Therefore, the number of words that Sofia will be tested on before the end of the year is 255. Question 3 Determine whether the statement makes sense or does not make sense, and explain your reasoning. Find the hardest part in solving a word problem is writing the equation that models the verbal conditions. Answer Assume there are 𝑁 N families. We have said that 24 of the sample families watched television for no more than 20 hours each week. The statement is true; it makes sense. Reason: Since the supplied statement is a compound statement that is recognized mathematically, it makes sense or is legitimate. A statement made up of two or more other statements is known as a compound statement. The statement claims that creating the equation from verbal or modeled data is the most difficult step in solving a word problem. Question 4 You can use systems of linear equations to solve word problems. First, define variables. Then model the situation with a system of linear equations. The difference between the measures of two complementary angles is 36. Find both angle measures. Answer Let 𝑥 x = the first angle Let 𝑦 y = the second angle The difference between the measures of two complementary angles is 36 ° 36°: 𝑥 − 𝑦 = 36 x−y=36 Two angles are complementary if the sum of their measures is 90 ° 90°: 𝑥 + 𝑦 = 90 x+y=90 Step 1: Eliminate 𝑦 y because the sum of the coefficients of 𝑦 y is zero. 𝑥 − 𝑦 = 36 𝑥 + 𝑦 = 902 𝑥 = 126 (Addition Property of Equality) 𝑥 = 63 (Solve for  𝑥 ) x−y=36x+y=902x=126(Addition Property of Equality)x=63(Solve for x) Step 2: Solve for the eliminated variable by using either of the original equations. 𝑥 + 𝑦 = 90 Choose the first equation 63 + 𝑦 = 90 Substitute  𝑥 = 63 𝑦 = 27 (Subtract 63 from both sides) x+y=90Choose the first equation63+y=90Substitute x=63y=27(Subtract 63 from both sides) The measures of the angles are 63 ° 63°, 27 ° 27°.