Word Problems Flashcards
(46 cards)
What does ‘is’ mean?
=
What does ‘was’ mean?
=
What does ‘has been’ mean?
=
What does ‘more’ mean?
+
What does ‘years older’ mean?
+
What does ‘years younger’ mean?
-
What does ‘less’ mean?
-
What does ‘times’ mean?
x
What does ‘less than’ mean?
-
What does ‘fewer’ mean?
-
What does ‘as many’ mean?
x
What does ‘factor’ mean?
x
how to solve age problems
- define variables for the ages in the present day
- represent each age in the future or in the past
- Organize the information from steps 1 and 2 in a matrix, with the columns representing the present, past, or future ages and the rows representing people or objects.
4: Use the information in the matrix as well as the problem stem to create corresponding equations for the present and future or past, and then use those equations to determine the answer.
Difference between variable and fixed costs?
Variable costs increase as more product is sold, but fixed costs do not.
When a company has both fixed and variable costs, the profit equation can be expanded to
profit = revenue - [total fixed costs + total variable costs]
formula for when two people transfer money to each other to equalize hourly wages
When two people earn $n each and $x is transferred from person A to person B to equalize their hourly wages, the formula is:
n-x/person a’s hours = n+x/person b’s hours
Fraction questions to find remaining portion
If you are given fractions, minus the remaining fraction from the whole. after youve done that for all of the portions that were taken, times those all together to find total remaining.
Example: One Sunday morning, a man is leisurely sitting in a coffee shop about to enjoy his full cup of gourmet coffee. During his first hour in the coffee shop, he drinks 1/4 cup of his coffee. During his second hour, he drinks 2/3 of his remaining coffee. During his third hour, he drinks 3/5 of the remaining coffee. What fraction of his coffee remains after three hours?
hour 1: 1-1/4: 3/4
hour 2: 1-2/3: 1/3
hour 3: 1-3/5: 2/5
times: 3/4 * 1/3 * 2/5 = 6/60 = 1/10 of remaining after three hours
general formula for remaining portion
The store began with x cell phones. After selling 1/y of the x cell phones, the store had x - 1/y * x cell phones in stock. simplified, the formula is x(y-1)/y where x is the total stock and y is the portion removed
Compound interest formula
A = P(1 + r/n)^n*t
A= future value
P = initial value [principal]
r = annual interest rate [expressed in decimal form]
t = number of years. if months, put over /12
n = number of compounding periods per year
constant growth formula
F = kn + p
F = final value
p = initial value
k = constant increase during each period
n = number of periods during which the growth occurs
exponential growth formula
final value = initial value( 1 + growth rate)^# of intervals
for growth questions, can one assume growth driver?
No. In order to determine the amount of growth, we must be presented with the growth driver.
When breaking down dry mixture problem, we need to consider three attribuets
- components of the mixture [what the mixture contains]
- the units of each component [e.g. dollars per pound]
- the quantitiy of each component
from there, create a matrix with the info.
- the components should consist of the left hand column
- the units should be the second column
- the quantity should be the third column
- the fourth column should be some sort of total [e.g. price]
- bottom row final mixture
IMPORTANT MATRIX NOTE:
- to find ‘total’ in last column, multiple quantities in rows
- for different solution ‘totals’, sum those and set equal to the final mixture [last row] product that you found earlier
When breaking down wet mixture problem, we need to consider three attributes
- components of the mixture [what the mixture contains]
- the concentration of each component [e.g. dollars per pound]
- the quantitiy of each component
from there, create a matrix with the info.
- the components should consist of the left hand column rows
- the concentations should be the second column
- the quantity should be the third column
- the fourth column should be some sort of total
- bottom row final mixture
IMPORTANT MATRIX NOTE:
- to find ‘total’ in last column, multiple quantities in rows
- for different solution ‘totals’, sum those and set equal to the final mixture [last row] product that you found earlier
‘up to’
≤
less than or equal to
