Question 3 31 the following problem was given to a grade 9...

Name: question 3 31 the following problem was given to a grade 9 class tickets for a school concert are sold at r6 for children and r10 for adults the total number of children and adults that will 71319
Uploaded: 2024-07-02T20:41:10-08:00
Duration: 6 min 13 s
Channel: Tanya Chase
Description: question 3 31 the following problem was given to a grade 9 class tickets for a school concert are sold at r6 for children and r10 for adults the total number of children and adults that will 71319

Question 3 3.1 The following problem was given to a Grade 9 class: 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. (2) 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. (2)

Transcript

00:01 All right, for this problem, we want to start by finding two numbers whose sum is 43 and whose difference is 5.

00:07 So we're going to let x equal the larger number, and we're going to let y equal the smaller number.

00:19 So we know that their sum is 43, so x plus y equals 43.

00:26 And we know that their difference is 5, so x minus y has to equal 5.

00:31 So now we have a system of equations to solve and they're already set up for us to use elimination.

00:38 So i'm going to add down my columns here.

00:40 X plus x is 2x.

00:43 Y plus negative y is just zero.

00:45 So i'll leave that be.

00:46 And then 43 plus 5 is 48.

00:50 So that lets x be 40.

00:54 Sorry, 24 because i'm going to divide both of those sides by 2.

00:58 All right.

00:58 So now i know what x is.

01:00 So i can plug that into either one of these equations.

01:03 So i can say 24 plus y is equal to 43.

01:08 So i'll subtract 24 from both sides to get that y is equal to 19.

01:13 And in fact, when x is 24 and y is 19, those are also five apart from each other.

01:19 So we found x and y there.

01:22 All right, for the next part of this, they want to find the value of x.

01:26 If the product of x plus 3 and 2x plus 3.

01:29 So that product would look like this, x plus 3 times 2x plus 3.

01:35 And that product is, is as always our equal sign, 14 more than the product of x plus 1 times 2x plus 1.

01:49 All right, so we're going to distribute through our parentheses.

01:52 So first we give the x value to each of these.

01:56 So x times 2x is 2x squared.

01:59 X times 3 is 3x and we're going to multiply the 3 to both of those.

02:04 So 3 plus 2x is 6x and 3 times 3 is 9.

02:10 And that's going to be equal to 14 plus, and we'll do our distribution again.

02:15 So x times 2x is 2x squared.

02:18 X times 1 is just x.

02:21 1 times 2x x is 2x and 1 times 1 is 1.

02:26 All right, now we can look to see where we can combine terms, but what's really nice is i see that this side has a 2x squared and this side has a 2x squared.

02:35 So if i were to subtract that, anything i do on one side i have to do on the other, that gets rid of my x squared value, which is nice because then i know i don't have to solve a quadratic.

02:45 So let's just go back and combine like terms on each side.

02:48 So 3x plus 6x is 9x plus the 9 that was already there is equal to, so, x plus 2x is 3x, and 14 plus 1 is 15.

03:01 So, i'm going to subtract 3x from both sides, and i'm going to subtract 9 from both sides to get all my letters on one side and all my numbers on the other side.

03:11 So, 9x minus 3x is 6x, and that's going to be equal to 6...

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