Word problems Flashcards
(20 cards)
What do I need to understand about wall of text…
What relationships are they revealing and how can they be translated into equations. Can I turn the “ask” into an equation to solve for
Glance at answer choices to see if…
they are whole numbers, mixed or contain variables. If spread out enough I can estimate.
Translating can only be done when…
quantities have identical units
Profit =
Revenue =
p = revenue - cost
R = Unit price * quantity
How would you translate the following into an equation? 4 kids pick up 33 candies, 1 kid picks up 3 fewer than the others
4x - 3 = 33
When given quotes on total cost for 2 items…
Price of A * Units of A + Price of B * Units of B
I can use the elimination method by subtracting one equation from another
Set up an IQ,
How many games can I attend based on $1000 season ticket that includes 2 free games and it costs 300 per additional one. I have a $4000 budget.
1000 + 300 (x-2) Less than or equal to 4000
Multiplication/Division in story context: when all quantities are associated with a unit do ___
Treat them like a variable as it gets manipulated alongside its coefficient
“per” reveals what relation? And can be translated to what?
Division… from a fraction to a ratio. Like Miles per galloon or books read per week
Explain conversion factor (AKA Rate) and apply the cancellation property to solve
Exp. how many minutes in 2 days
Units in Q * conversion factor = answer
2 days * 24 hours per day = days cancel out, 2 * 24 is 48 hours total
48 hours * 60 minutes per hour = hours cancel out 48 * 60 minutes total
Translate “I walk x miles, how many KM is that?”
X miles * KM per mile = answer
What is the Rate Time Distance formula? Similar to total cost equation
Rate * Time = Distance
Can be changed algebraically
Rate = D / T
Price per unit * Quantity = Cost
Work problems are similar to RTD except you substitute…
rate for productivity… one unit of productivity per time lapsed
When 2 people are working together at the same time towards a goal…
Solve:
Alex completes a chair in 3 hours and John does it in 5
Sum their rates, interpreted they build x amount of the finished good per this much time together OR they complete the job per that much time
Alex is 1/3 of the way done in an hour or completely done in 3 hours
During the U phase…
- Think should I work backwards or Rephrase and simplify
- Pay attention to Units, in additive relationships you can only use identical ones
Multiplication of units can…
change as things get simplified. Like with rates or unit costs
Why are conversion factors so useful…
they cancel the units you don’t want to remain, that are not being asked for
Solve this with conversion factors…
A patient takes 3 days of medicine. It requires 4 doses daily and each dose contains 150 MG’s. How many total MG’s are used.
3 days * (4 doses / day) * (150MG/ dose)
with the first CF you get 12 total doses
The second reveals 150 MG per dose and cancels out the final unit “doses”
I am given an unusual story…
draw it out! Use logic
When maximizing and minimizing amounts there are rounding implications, what are good rules?
- You can’t have fractions of people so if says the maximum is a mixed integer you would round down (50/3)
- Always find the most constrained group during the P phase
