Word Problems Flashcards
What is the smart number strategy process? WP59
- 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 - solve problem using SN. circle answer
- replace all variables w/ your SN in the answers and see which matches with your answer. careful as multiple ac might match
When do you use smart numbers? WPSG60
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
Common Relationships to memorize:
Total Cost Profit Total earnings Miles Miles
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
Conversion factors WPSG20
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.
What is the process to work backwards?
When do you WB?
- Start with ac B or D
- 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.
How do you find the avg rate of two trips?
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
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?
could be # of jobs done or items produced
RT=W
How do you solve a prb that has 2 things working together?
Working together? add rates
If one is undoing the work? subtract rates
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?
If sets are precents-> use 100 as total
If they’re fractions: choose a common denom for the total
Draw table. Answer is 1.
REMEMBER:
Read the problem carefully
Draw tables to keep organized
work from AC if you get stuck!
x
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
(Rate of A - Rate of B) x T= diff of distance
OR set up the two rt=d equations and substitute.
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
(Rate of A - Rate of B) x T= diff of distance
OR set up the two rt=d equations and substitute.
How do you find the combined rate for 2 machines productivity when you know each of their individual rates?
You add the rates to complete the same amount of work, together.
Rate of A + Rate of B= Combined Rate
How do you solve a matrix problem when it asks for a specific amount but gives you percents for data?
Use a variable (x) in each of the boxes to signify a percent of something.
How do you find the time at which one car will outpace another car by a certain distance?
You subtract the rates to get the relative rate. This will tell you how rapidly the distance between them grows.P284, DS106.