Word Problems Flashcards

1
Q

What is the smart number strategy process? WP59

A
  1. Choose SN to replace the variables in Q. are they tied to each other? If so one would determine the number for the other.
    - pick different numbers with diff characteristics
    - follow any constraints
    - choose numbers that would work easily
    - box off the numbers you choose on your paper
  2. solve problem using SN. circle answer
  3. replace all variables w/ your SN in the answers and see which matches with your answer. careful as multiple ac might match
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2
Q

When do you use smart numbers? WPSG60

A

When problem contains only unspecified values and has variables in the answer choices. And when AC not only have variables, but also have percents or fractions.
dont choose numbers: that are in the problem, solve to give you a number that was in the problem, 0 or 1

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3
Q

Common Relationships to memorize:

Total Cost
Profit
Total earnings
Miles
Miles
A
Total Cost ($)= unit price ($/unit)x Quantity (units)
Profit ($)= Revenue ($)-Cost ($)
Total Earnings ($)= Wage rate ($/hr) x Hrs worked (hrs)
Miles= Miles per hr X Hours
Miles= Miles per gallon x Gallons
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4
Q

Conversion factors WPSG20

A

A fraction who’s numerator and denominator have different units but are the same value eg 60sec/1minute. Use them to cross out units you dont need to get to the units you need.

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5
Q

What is the process to work backwards?

When do you WB?

A
  1. Start with ac B or D
  2. draw chart: label AC with what you are solving for.
    when to WB: ACs are numerical and nice #s (small, all even). Question asks for an exact number that can be labeled w/ 1 variable.
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6
Q

How do you find the avg rate of two trips?

A

Avg speed= Total Distance/Total time
*Avg is not the avg of the two rates. It will always be closer to the slower of the two.
If a common distance is not listed, pick a SN multiple of the 2 rates

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7
Q

What is the equation for work? Solve:
Martha can paint 3/7 of a room in 4.5 hours. If Martha finishes painting the room at the same rate, how long will it have taken Martha to paint the entire room?

A

could be # of jobs done or items produced

RT=W

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8
Q

How do you solve a prb that has 2 things working together?

A

Working together? add rates

If one is undoing the work? subtract rates

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9
Q

Overlapping sets WPSG69
Of 30 integers, 15 are in set A, 22 are in set B, and 8 are both in set A and B. How many of the integers are in neither set A nor set B?

A

If sets are precents-> use 100 as total
If they’re fractions: choose a common denom for the total
Draw table. Answer is 1.

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10
Q

REMEMBER:
Read the problem carefully
Draw tables to keep organized
work from AC if you get stuck!

A

x

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11
Q

relative rate equation:
PS207: Car A is 20mi behind CarB which is traveling the same direction along the same route as Car A. Car A is traveling at a constant speed of 58mi per hour and car B is traveling at a constant speed of 50mi per hour. How many hours will it take for car A to overtake and drive 8 mi ahead of Car B

A

(Rate of A - Rate of B) x T= diff of distance

OR set up the two rt=d equations and substitute.

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12
Q

relative rate equation:
PS207: Car A is 20mi behind CarB which is traveling the same direction along the same route as Car A. Car A is traveling at a constant speed of 58mi per hour and car B is traveling at a constant speed of 50mi per hour. How many hours will it take for car A to overtake and drive 8 mi ahead of Car B

A

(Rate of A - Rate of B) x T= diff of distance

OR set up the two rt=d equations and substitute.

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13
Q

How do you find the combined rate for 2 machines productivity when you know each of their individual rates?

A

You add the rates to complete the same amount of work, together.

Rate of A + Rate of B= Combined Rate

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14
Q

How do you solve a matrix problem when it asks for a specific amount but gives you percents for data?

A

Use a variable (x) in each of the boxes to signify a percent of something.

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15
Q

How do you find the time at which one car will outpace another car by a certain distance?

A

You subtract the rates to get the relative rate. This will tell you how rapidly the distance between them grows.P284, DS106.

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16
Q

What should you do when they give you easy percentages in a word problem?

A

Convert to fractions to make it easier to solve!

17
Q

What should you do when you see twins in the answer choices?

A

One is good and the other one is evil- Find the good twin and pick that answer.

18
Q

What are the 2 approaches to solving Rate problems?

A
Rate Table (RxT=d) PS119
Real Life: draw it out and solve. You can solve backwards too. 

DO NOT “think through” word problems, write and draw it out.

You can also use algebra

19
Q

What is the “Make It Real” strategy?

A

Drawing it out and either using numbers so you full understand word problems

20
Q

What should you use for an overlapping set problem?

A

Double set matrix. Be careful in filling out the right box with the right information.