Ch. 6, 7, 8, 9 Word Problems Flashcards
Translate to math: “Liz has 50 fewer friends than Selby does”
L = S - 50
If you get an age problem (e.g., “Harry is 3 times as old as Paul. In five years, the sum of their ages will be 50. How old is Harry now?”), what is the process to solve?
Create a matrix with today’s ages (H & P) and future ages (H+5 and P+5) then create equations based on that & solve:
H = 3P
(H+5)+(P+5)=50
H = 30
Plug these into the profit equation: biz insurance is $200, you sell each widget for $5, it costs you $2 per widget.
Profit = Revenue - [Fixed Cost + Variable Cost]
Number of widgets sold = n
Revenue = 5n
Variable Cost = 2n
Fixed Cost = 200
How to equalize rates (salary, price, miles, etc.)
Get the rates, e.g., 100/5 and 140/10
Then add x to one and subtract x from the other
(100 - x) / 5 = (140 + x) / 10
What is the process for solving a fraction of a fraction word problem?
Create two columns: amount consumed, amount remaining. Key is to stay organized.
Simple interest formula
Interest = Principal x Rate x Time
Make sure time & rate are same units
If rate is a variable (e.g., “interest rate is x”), make sure you do x/100 in the formula.
Compound interest formula
A = P (1 + r/n) ^(nt)
A = future value
P = initial value
r = rate (decimal) per year
n = compounding periods per year
t = time (number of years)
2, 4, 6, 8,.. what is the next number?
You CANNOT predict the next number!! unless the problem specifically gives you the growth factor, DO NOT ASSUME
Linear growth formula
F = p + kn
F = final value
p = initial value
k = growth constant
n = number of growth periods
Exponential growth formula
initial value x (growth factor)^(growth period)
When is decay the greatest?
Usually in the first period (b/c that’s when there’s the most of the item still remaining)
How to represent consecutive integers
Represent the first integer as x
Then add the numbers accordingly:
If consecutive, x+1, x+2, etc.
If even/ odd, x+2, x+4, x+6, etc.
If multiples of 7, x+7, x+14, x+21, etc.
When there are people in a line, what do you need to be careful of?
Don’t double count yourself.
Usually if someone is 10th from the front and 15th from the back, you can do
n + m - 1 = 10 + 15 - 1 = 24
OR just figure it out: 9 people ahead of him, himself, 14 people behind = 9 + 1 + 14 = 24
How to do a mixture question?
Identify the components, units (or concentration) and quantities. Then create a matrix.
Last column is total; Bottom row is always “final mixture”
Average Rate
Total Distance / Total Time
