Math 131!
Word Problems! Prerequisite: None
Course Description
During this micro-course, students will translate word problems into mathematic expressions, and then solving those questions using a variety of methods and strategies. !
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Translation Problems
Translation Problems! ! Identify:! Look for word problems with no given equation.! ! Set Up:! Use the following chart to write the equation:! ! Make Sure:! Watch out for “less than”: the number you are subtracting is often written in the question BEFORE the value you are subtracting it from.! ! Execute:! Solve the equation you have written.!
Math 131
WHAT
variable (x, y, etc.)
IS
equals
OF
times
PERCENT
divided by 100
MORE THAN
plus
LESS THAN
minus
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Translation Problems
Example:! What percent of 25 is 25 percent of 20? (A) 120 (B) 100 (C) 50 (D) 25 (E) 20
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Plug and Chug Problems
Plug and Chug Problems! ! Identify:! Look for word problems with variables in the question and in the answer choices.! ! Set Up:! PLUG: Pick simple numbers to plug in for each of the variables.! ! Make Sure:! Keep your numbers straight – write down which numbers go with which variables.! ! Execute:! CHUG: Solve the situation described in the question using your numbers. ! PLUG: Then plug the numbers into each of the answer choices. !! CHUG: Eliminate answer choices that differ from the solution you got for the question.!
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Translation Problems
Example:! The sum of two numbers that differ by three is y. In terms of y, what is the value of the lesser of the two numbers? (A) (B) (C) (D) (E)
y+3 2 y 2 y −3 2 y −3 2 2y + 3 2
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Review Questions If q is 20 percent greater than p, and p is 35 percent greater than 2,000, what is the value of q – p ? (A) (B) (C) (D) (E)
5,940 3,240 2,700 540 300
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Review Questions If m is a positive even integer, which of the following must represent an integer that is evenly divisible by 4 ? (A) m + 2 (B) 2m – 2 (C) 2m + 3 (D) m2 + 8 (E) m2 – 10
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Review Questions If 3a + b is 150 percent of 8a, what is the value of
b ? a
(A) 1.5 (B) 3 (C) 6 (D) 8 (E) 9
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Review Questions Coffee leaks out of a container at the rate of l liters in h hours. If the coffee costs 8 dollars per liter, how much money, in dollars, will be lost in x hours? (A) (B) (C) (D) (E)
8h lx lx 8h 8lx h lh 8x hx l
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Review Questions If 2 more than 4 times a number is equal to 12, what is 3 times the number? (A) 2
1 2
(B) 5 1 2 (D) 10 (C) 7
(E) 12
1 2
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Review Questions Which of the following equations correctly represents the statement “three less than twice a number is the same as eight more than half the number?” x
(A) 3 – 2x = 8 + 2 (B) 2 – 3x = x + 4 (C) 2x – 3 = 4 + x 1
(D) 3x – 2 = 2 x + 8 1
(E) 2x – 3 = 2 x + 8
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Review Questions Eight coworkers are involved in an office holiday gift exchange. Two of these coworkers are male, and the rest are female. If everyone puts their names into a hat, what is the probability that the first name drawn from the hat will belong to one of the female coworkers? 1 4 1 (B) 3 1 (C) 2 2 (D) 3 3 (E) 4 (A)
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Review Questions A group of 8 people go out to eat at a local restaurant. At the end of the meal, the group realizes that their final bill includes a gratuity equal to 18% of their total purchases. If their final bill is $72.00, what was the total cost of their purchases, in dollars, before the gratuity was added? (A) $12.96 (B) $35.06 (C) $54.00 (D) $61.02 (E) $84.96
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Review Questions Last week, Kira ran 10 miles fewer than Marcus, and this week Kira ran 7.5 miles more than Marcus. Which of the following must be true about Kira's total miles run for the two weeks compared to Marcus’? (A) (B) (C) (D) (E)
Kira ran 17.5 miles fewer than Marcus. Kira ran 2.5 miles fewer than Marcus. Kira ran 2.5 miles more than Marcus. Kira ran 17.5 miles more than Marcus. Kira ran half as many miles as Marcus.
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Review Questions Sam bought a shirt. Two years later, he sold the shirt to a second-hand store for 40 percent less than he paid for it. The store then added 20 percent onto the price it paid and resold it. What percent of the original price paid by Sam is represented by the price this last customer paid for the shirt? (A) 40% (B) 60% (C) 72% (D) 80% (E) 88%
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Review Questions While making dinner, Sydney peeled one third of p potatoes, Josh peeled three times as many potatoes as Sydney, and Britney peeled 10 fewer potatoes than Josh. In terms of p, how many potatoes did Britney peel? (A) p + 10 (B) p − 10 p + 10 (C) 3 p (D) − 10 3 p (E) + 10 3
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Review Questions The manager of a sporting goods store runs a special “30 percent off sale” during the weekend. On Monday morning, he decides to increase all of the sale prices by 30 percent. If a sleeping bag cost $80 before the weekend sale, what is the cost of the sleeping bag on Monday, after the price increase (to the nearest dollar, excluding tax)? (A) (B) (C) (D) (E)
$104 $80 $77 $73 $56
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Review Questions For every house he sells, a realtor receives a commission that is equal to p% of the house’s selling price. Which of the following represents the total commission he receives, in dollars, if he sells two houses for $400,000 each? (A) 8,000p (B) 200,000p (C) 800,000p 800, 000 p 400, 000 (E) 100 + 2 p
(D)
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Review Questions If k is a positive even prime integer and n is a negative odd integer, which of the following CANNOT be a positive integer? (A) (B) (C) (D) (E)
k+n k–n nk kn 2k – 2n
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Review Questions A museum charges different rates for adult and child tickets. If 2 adult tickets and 1 child ticket cost $18.50, while 1 adult ticket and 2 child tickets cost $16.00, what is the total cost of 3 adult tickets? (A) (B) (C) (D) (E)
$4.50 $7.00 $13.50 $21.00 $34.50
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Review Questions Paul has been a doctor for 3 years more than half as long as Nancy has been a doctor. If Nancy has been a doctor for x years, which of the following expressions represents the number of years that Paul has been a doctor? x −3 2 x (B) +3 2 (C) 2 x − 3 (A)
(D) 2 x + 3 (E) 3 − 2 x
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