Word Problems

Question 1

What does ‘is’ mean?

Answer 1

=

Question 2

What does ‘was’ mean?

Answer 2

=

Question 3

What does ‘has been’ mean?

Answer 3

=

Question 4

What does ‘more’ mean?

Answer 4

+

Question 5

What does ‘years older’ mean?

Answer 5

+

Question 6

What does ‘years younger’ mean?

Answer 6

-

Question 7

What does ‘less’ mean?

Answer 7

-

Question 8

What does ‘times’ mean?

Answer 8

x

Question 9

What does ‘less than’ mean?

Answer 9

-

Question 10

What does ‘fewer’ mean?

Answer 10

-

Question 11

What does ‘as many’ mean?

Answer 11

x

Question 12

What does ‘factor’ mean?

Answer 12

x

Question 13

how to solve age problems

Answer 13

1. define variables for the ages in the present day
2. represent each age in the future or in the past
3. 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.

Question 14

Difference between variable and fixed costs?

Answer 14

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]

Question 15

formula for when two people transfer money to each other to equalize hourly wages

Answer 15

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

Question 16

Fraction questions to find remaining portion

Answer 16

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

Question 17

general formula for remaining portion

Answer 17

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

Question 18

Compound interest formula

Answer 18

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

Question 19

constant growth formula

Answer 19

F = kn + p

F = final value
p = initial value
k = constant increase during each period
n = number of periods during which the growth occurs

Question 20

exponential growth formula

Answer 20

final value = initial value( 1 + growth rate)^# of intervals

Question 21

for growth questions, can one assume growth driver?

Answer 21

No. In order to determine the amount of growth, we must be presented with the growth driver.

Question 22

When breaking down dry mixture problem, we need to consider three attribuets

Answer 22

1. components of the mixture [what the mixture contains]
2. the units of each component [e.g. dollars per pound]
3. 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

Question 23

When breaking down wet mixture problem, we need to consider three attributes

Answer 23

1. components of the mixture [what the mixture contains]
2. the concentration of each component [e.g. dollars per pound]
3. 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

Question 24

‘up to’

Answer 24

≤
less than or equal to

Question 25

'more than'

Answer 25

'>' greater than

Question 26

at least

Answer 26

≥ greater than or equal to

Question 27

'exceed'

Answer 27

'>' greater than

Question 28

'no more'

Answer 28

≤ less than or equal to

Question 29

'at most'

Answer 29

≤ less than or equal to

Question 30

'as few as'

Answer 30

≥ greater than or equal to

Question 31

counting objects in a line formula

Answer 31

In general, if you (or anyone) are the mth person counted from the beginning of the line and the nth counted from the end, then the number of people waiting in line is m + n -1

Question 32

formula for distance

Answer 32

distance = rate * time

Question 33

formula for time

Answer 33

time = distance / rate

Question 34

formula for rate

Answer 34

rate = distance / time

Question 35

average rate for an entire trip

Answer 35

distance 1 + distance 2...etc / time 1 + time 2 ... etc

Question 36

formula for total distances for converging objects

Answer 36

distance object 1 + distance object 2 = total distance objects 1 and 2 in practice: Thorstein is in Easton and Tom is in Weston, two towns that are 240 miles apart. Thorstein and Tom leave their respective towns at the same time and drive toward each other on the same road. If Thorstein drives at a constant speed of 60 miles per hour and Tom drives at a constant speed of 40 miles per hour, how many minutes will it take before Thorstein and Tom meet each other on the road? Thorstein: distance = 60t Tom: distance = 40t 60t + 40t = 240 100t = 240 t= 12/5 hours, or 144 minutes

Question 37

formula for total distances for diverging objects

Answer 37

distance object 1 + distance object 2 = total distance objects 1 and 2

Question 38

Setting up variable for distance for round trip problems

Answer 38

In a round-trip problem when only the total time traveled is provided, consider letting the time to a destination equal some variable t and the time back equal (total trip time - t). set each leg of the trip equal to each other to solve

Question 39

formulas where objects catch up and pass each other

Answer 39

1. faster object's distance = slower objects distance + (difference in starting points + difference in ending points) 2. time = change in distance (difference in starting points + difference in ending points) / change in rate (difference in rate of two objects)

Question 40

what is relative motion

Answer 40

An object travels relatively faster when it is moving along with an outside force than when it is traveling under its own power. Conversely, an object will move relatively slower when it is moving against an outside force than when it is moving under its own power. Example, if airplane is traveling at 500 MPH and flies along with wind that is blowing at 50 MPH, its speed is 550 MPH relative to ground

Question 41

formula to find rate, gas/energy used, distance

Answer 41

rate * gallon = distance

Question 42

distance is directly proportional to rate and time

Answer 42

if rate increases and time remeains constant, distance increases if time increases and rate remains constant, distance increases

Question 43

rate is inversly proportional to time and directly proportional to distance

Answer 43

if rate increases time to travel distance decreases and vice versa if rate increases, distance increases

Question 44

time is inversly proportional to rate and directly proportional to distance

Answer 44

if time to travel increases rate decreases and vice versa if time increases, distance increases

Question 45

Setting up variables for time for two objects when both start a task but one stops and the other must finish the job alone

Answer 45

let the time for the object that stops first represent 'x' and the work time for the object that finishes the job be 'x+y' with y being the remaining time needed

Question 46

Basic formula for setting up work rate variables when two objects are working against each other

Answer 46

1/x - 1/y