OG 12th Problem Solving 41-60

Question 41 – “If 4 is one solution of the equation…”
OG Explanation is fine. Another way to do this problem:
x² + 3x + k = 10
x² + 3x + (k – 10) = 0
Since 4 is a solution, the previous equation can be factored
( x – 4 ) ( x + b ) = 0
In order to get the positive 3x, we must have the other term to be ( x + 7 ); thus the other solution is -7.
Khan Academy Link OG 11th #38 - Begins at 3:20

Question 42 – “If matrix a b c d = ad-bc…”
OG Explanation is fine. (trivia: ad-bc in this matrix is called the determinant of the matrix

Question 43 – “The sum 7/8 + 1/9….”
OG Explanation is fine.

Question 44 – “If x = 1 – 3t and y = 2t – 1…..”
OG Explanation is fine.
Khan Academy Link OG 11th #38 – Begins at 8:20 (The answer is D not A, I think there is a mistake on the Khan site)
Problem 41

Question 45 – “1- (1/2 – ….”
OG Explanation is fine.

Question 46 – “(0.3)^5 / ….”
OG Explanation is fine
Khan Academy Link OG 11th #43 – Begins at 1:20

Question 47 – “In a horticultural experiment, 200 seeds were planted….”
OG Explanation is fine. Note that you could view this as a weighted average problem.
Khan Academy Link OG 11th #44 – Begins at 2:40

Question 48 – “In the figure above…”
OG Explanation is fine, but it may be easier to draw it out.

Question 49 – “How many integers n are there such….”
OG Explanation is okay, but I don’t think direct algebra is necessary here.
Khan Academy Link OG 11th #46 – Begins at 7:05

Question 50 – “If y is an integer then the least…”
OG Explanation is too complex. Notice that the questions is not asking for the value of y, rather it is asking for the lowest possible value of the expression. Since the absolute value is the distance from 0 on the number line, we know that 23-5y must be close to 0. The closest value are at y=4 or y=5. When y=4, the expression is 3; when y=5, the expression is 2. Thus the minimum value is 2.

Question 51 – “Sqrt of 7 + ….”
OG Explanation is fine.
Khan Academy Link OG 11th #49 - Begins at 0:00

Question 52 – “In a certain population, there….”
OG Explanation is okay. Alternatively, you could just pick numbers. Suppose there is 1 person over 21, then there are 3 people 21 or under. There are a total of 4 people here. Thus, the ratio of those 21 or under to the total population, is 3 to 4.
Khan Academy Link OG 11th #50 – Begins at 0:55

Question 53 – “In the figure above…”
OG Explanation is fine.
Khan Academy Link OG 11th #51 – Khan 3:00

Question 54 – “sqrt 80 + sqrt 125 ….”
OG Explanation is fine. You may want to prime factorize 80 and 125.

Question 55 – “Kelly and Chris packed several…”
OG Explanation is fine. Alternatively, you can just pick numbers. For percent problems, it is good to pick 100 as a starting number. If there are 100 boxes and Chris packed 60%, he packed 60 books. Kelly packed the remaining 40 boxes. The ratio of the # of boxes Kelly packed to the # of boxes Chris packed is 40 to 60, which simplifies to 2 to 3.
Khan Academy Link OG 11th #52- Begins at 5:05

Question 56 – “Of the following…”
OG Explanation is fine.
Khan Academy Link OG 11th #53 – Begins at 6:35

Question 57 – “The average (arithmetic mean) of 10, 30 … ”
OG Explanation is fine.
Khan Academy Link OG 11th #54 Khan – Begins at 7:35

Question 58 – “In this equation above, k is a constant…..”
OG Explanation is fine.

Question 59 – “Each week, Harry is paid x dollars….”
OG Explanation is fine but I think it is easier to just pick numbers. If x = $10, James earned 40($10) + 1($20) = $420 for working 41 hours. Harry makes 30($10) = $300 for the first 30 hours he works. For any following hours he makes 1.5x or $15 per hour. For him to make the remaining $120 (i.e. $420 – $300), he must work 120/15 or 8 additional hours. Thus, he must work 38 hours to earn the same amount as James.

Question 60 – “A glass was filled with 10 ounces of water…”
OG Explanation is fine.


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