Tickets for a school concert are sold at R6 for children and R10 for adults. The total number of children and adults that will attend the concert is 150. A total of 150 people attended the concert, and the total entrance fees collected amounted to R1,100.
Determine how many children attended the concert.
Two students, Sam and Thabo, attempt to solve the problem.
Sam's Algebraic Attempt:
Let c = number of children
Let a = number of adults
Eq 1: c + a = 1100
Eq 2: 6c + 10a = 150
(Sam gets stuck and cannot proceed.)
Thabo's "Trial and Improvement" Attempt:
"I know 150 people attended. I'll guess 100 children and 50 adults."
Calculation 1: (100 x R6) + (50 x R10) = R600 + R500 = R1,100.
"Oh, I got it on the first try! So, 100 children."
As a student teacher, analyse their work:
3.1.1 Identify the conceptual error in Sam's setup of the algebraic equations. Explain what this error reveals about his understanding.
3.1.2 Thabo found the correct answer using a method of trial and error. Briefly explain why this is a valid, though not always efficient, problem-solving strategy.
Answer (2)
Sam's first equation incorrectly states the total number of attendees as 1100 instead of 150, which shows a misunderstanding of the problem. Thabo's trial and error successfully yielded the correct answer on his first guess, demonstrating a valid but potentially inefficient strategy. For the correct approach, the equations should be set up as c + a = 150 and 6c + 10a = 1100.
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3.1.1 Sam's setup of the algebraic equations contains a conceptual error in the first equation, where he states: c + a = 1100 This equation is incorrect because it indicates a total of 1100 people attending the concert, which contradicts the problem statement that only 150 people attended. The correct equation should be: c + a = 150 This error reveals that Sam misunderstood the problem's statement about the total number of attendees. Instead of recognizing that 150 is the total number of people, he mistakenly took 1100, which is the total amount of money collected.
3.1.2 Thabo's trial and improvement method is a valid strategy because it involves making educated guesses and checking if those guesses satisfy all given conditions of the problem. Even though he found the correct answer on his first try, trial and error might not always be efficient as it can be time-consuming and rely on luck or intuition to quickly arrive at a solution. However, it can be a useful approach when dealing with smaller numbers or situations where other methods may seem too complex or not immediately obvious.
To summarize, the correct setup of Sam's algebraic equations should be:
c + a = 150
6 c + 10 a = 1100 Now, solving these equations can correctly determine the number of children.
