Word Problems

Question 1

“Is”

Answer 1

=

Question 2

“Was”

Answer 2

=

Question 3

“Has been”

Answer 3

=

Question 4

“More”

Answer 4

+

Question 5

“Years older”

Answer 5

+

Question 6

“Years younger”

Answer 6

-

Question 7

“Less”

Answer 7

-

Question 8

“Times”

Answer 8

X

Question 9

“Less than”

Answer 9

-

Question 10

“Fewer”

Answer 10

-

Question 11

“As many”

Answer 11

X

Question 12

“Factor”

Answer 12

X

Question 13

What are the 4 steps for solving age problems?

Answer 13

1. Define variables for ages in the present day
2. Represent each age in the future or the past
3. 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.
4. Use the info in the matrix as well as the problem stem to create equations, and then use those equations to determine the answer.

Question 14

If a board/rope were cut into 3 parts and those 3 parts were labeled x,y,z, then what must be true?

Answer 14

X+y+z= the total length.

Question 15

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?

Answer 15

$10(20) + $15(H-20)

Question 16

If you begin with x amount of anything and subtract 1/y of that amount… how much remains?

Answer 16

(x(y-1))/y will remain

Question 17

What is the formula for simple interest?

Answer 17

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

Question 18

What is the formula for compound interest?

Answer 18

Future Value of Investment =

Principal (1 + r/n) ^ (nt)

Where:
r= rate (in decimal form)
n= # of compounding periods per year
t= # of years

Question 19

What do you do when a compounding problem is too complex to solve (I.e. the mental math is hard)?

Answer 19

Look at the answers and see how far apart they are. If they are v far apart, estimate using simpler math!

Question 20

What is the linear growth function?

Answer 20

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

Question 21

What do you need to know about linear and exponential growth problems?

Answer 21

The growth driver!! Just because you see a pattern, doesn’t mean you can assume it’s the growth driver.

Question 22

What is the exponential growth function?

Answer 22

Initial amount * growth factor ^ (growth period)

Question 23

What happens when exponential decay occurs?

What period does the greatest amount of decay occur?

Answer 23

The amount of the decay decreases with each successive decay period.

The greatest decay occurs during the first period of decay.

Question 24

How do you algebraically represent a 2 digit number xy?

Answer 24

10x + y

Question 25

How do you algebraically represent consecutive integers?

Answer 25

Make the first integer x, then:

x 
x+1
x+2
x+3
.
.
.

Question 26

How do you algebraically represent consecutive even or consecutive odd integers?

Answer 26

Set the first integer in the set as x, then:

x
x+2
x+4
x+6
.
.
.

Question 27

How do you algebraically represent consecutive multiples of integers ; e.g. multiples of 3

Answer 27

Set the first multiple as x, then:

x
x+3
x+6
x+9
.
.
.

Question 28

What three attributes do you need to recognize in a dry mixture problem?

Answer 28

1) the components of the mixture
2) the units of each component
3) the quantity of each component

Question 29

What three attributes do you need to recognize in a wet mixture problem?

Answer 29

1) the components of the mixture
2) the concentration of each component
3) the quantity of each component

Question 30

“Up to”

Answer 30

<=

Less than or equal to

Question 31

“More than”

Answer 31

>

Greater than

Question 32

“At least”

Answer 32

> =

Greater than or equal to

Question 33

“Exceed”

Answer 33

>

Greater than

Question 34

“No more”

Answer 34

<=

Less than or equal to

Question 35

“At most”

Answer 35

<=

Less than or equal to

Question 36

“As few as”

Answer 36

> =

Greater than or equal to

Question 37

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?

Answer 37

the number of people waiting in line is m+n-1 (subtract 1 so you don’t double count yourself)

Question 38

Express as an equation: A is 1/2 longer than b.

Answer 38

A = 3/2*B