Word Problems Flashcards
“Is”
=
“Was”
=
“Has been”
=
“More”
+
“Years older”
+
“Years younger”
-
“Less”
-
“Times”
X
“Less than”
-
“Fewer”
-
“As many”
X
“Factor”
X
What are the 4 steps for solving age problems?
- Define variables for ages in the present day
- Represent each age in the future or the past
- Organize the info from steps 1-2 in a matrix with the columns representing the present, past or future ages and the rows representing people or objects.
- Use the info in the matrix as well as the problem stem to create equations, and then use those equations to determine the answer.
If a board/rope were cut into 3 parts and those 3 parts were labeled x,y,z, then what must be true?
X+y+z= the total length.
What is the formula for the total comp for the job if the job pays $10 per hour for the first 20 hours and $15 per hour for each subsequent hour?
$10(20) + $15(H-20)
If you begin with x amount of anything and subtract 1/y of that amount… how much remains?
(x(y-1))/y will remain
What is the formula for simple interest?
Interest = principal x rate* x time**
*Put this divided by 100 if it’s a percent
**If the rate is annual but asking for 8 months, do 8/12
What is the formula for compound interest?
Future Value of Investment =
Principal (1 + r/n) ^ (nt)
Where:
r= rate (in decimal form)
n= # of compounding periods per year
t= # of years
What do you do when a compounding problem is too complex to solve (I.e. the mental math is hard)?
Look at the answers and see how far apart they are. If they are v far apart, estimate using simpler math!
What is the linear growth function?
F(N) = kN + p
Where: F(N) is the final value after growth occurs p= the initial value k= constant increase / period n= number of periods
What do you need to know about linear and exponential growth problems?
The growth driver!! Just because you see a pattern, doesn’t mean you can assume it’s the growth driver.
What is the exponential growth function?
Initial amount * growth factor ^ (growth period)
What happens when exponential decay occurs?
What period does the greatest amount of decay occur?
The amount of the decay decreases with each successive decay period.
The greatest decay occurs during the first period of decay.
How do you algebraically represent a 2 digit number xy?
10x + y
How do you algebraically represent consecutive integers?
Make the first integer x, then:
x x+1 x+2 x+3 . . .
How do you algebraically represent consecutive even or consecutive odd integers?
Set the first integer in the set as x, then:
x x+2 x+4 x+6 . . .
How do you algebraically represent consecutive multiples of integers ; e.g. multiples of 3
Set the first multiple as x, then:
x x+3 x+6 x+9 . . .
What three attributes do you need to recognize in a dry mixture problem?
1) the components of the mixture
2) the units of each component
3) the quantity of each component
What three attributes do you need to recognize in a wet mixture problem?
1) the components of the mixture
2) the concentration of each component
3) the quantity of each component
“Up to”
<=
Less than or equal to
“More than”
>
Greater than
“At least”
> =
Greater than or equal to
“Exceed”
>
Greater than
“No more”
<=
Less than or equal to
“At most”
<=
Less than or equal to
“As few as”
> =
Greater than or equal to
If you are the m’th person counted from the beginning of the line and the n’th person counted from the end of the line, then what is the number of ppl waiting in line?
the number of people waiting in line is m+n-1 (subtract 1 so you don’t double count yourself)
Express as an equation: A is 1/2 longer than b.
A = 3/2*B
