General Word Problems

Question 1

Age Problems

Answer 1

1. Define Variables for ages in present day
2. Represent each age in future or past
3. Set-up system of equations
4. Solve for variable

Question 2

Length Problems

Answer 2

1. Assign a variable to each length (i.e. short, long)
2. Set up an equation adding lengths to total lengths and another equation that relates the lengths to each other
3. Solve for variable

Question 3

Word Problems with 2 variables

Answer 3

You can substitute a variable into both sides of the equation to help you remove 1 variable and allow you to solve for the other variable.

Question 4

Discounts

Answer 4

80% discount = Pay 20% of Price

$2,500 spent on tix with 80% = $2,500 x (5) = $12,500 worth of discounted tix

Question 5

Fractional Parts of Whole Must Sum to the Whole

Answer 5

To avoid negative carry mistakes use Total = P1 + P2 + P3… that way if P2 = P1 - (4/5)P, you avoid forgetting to distribute the negative.

Question 6

Compound Interest Formula

Answer 6

A = P (1+(r/n))^(nt)

A the is final value of principal plus interest

If the interest rate is giving as “y percent”, plug in (y/100) into r

Sometimes the question gives you only the interest earned, use A = P + I to solve for the variable needed.

Question 7

Linear Growth

Answer 7

y = mx + b

Question 8

Exponential Growth

Answer 8

Growth = Initial Value * Growth Factor^(growth periods)
Decay = Initial Value * (1/decay factor)^(growth periods)

Question 9

To determine the amount of growth, a growth driver must be know.

Answer 9

Ex:
The next number in the this sequence 2, 4, 6, 8… cannot be determined unless it’s given that the numbers are evenly spaced.

Question 10

Sum of consecutive integers, consecutive even integers, and consecutive multiples of integers

Answer 10

sum of four consecutive integers is x + (x+1) + (x+2) + (x+3) + (x+4) = 4x+6

sum of 3 even consecutive integers is x + (x+2) + (x+4) = 3x+6

sum 3 consecutive multiples of 5 is x + (x+5) + (x+10) = 3x+15

Question 11

Inequalities

Answer 11

As few as six = greater than or equal to six
at most five = less than or equal to five
at least = greater than or equal to

Question 12

Objects in a line

Answer 12

If you are the the nth person from the beginning of the line and the mth person from the end of the line. Total number of people in line is equal to m+m-1

Question 13

Common Mistakes/Understand the exactly what the question is asking for and the answers provided.

Answer 13

Understand exactly what the question is asking for. Look out for x old vs. x new. You might solve for x old but you need to find x new.

You might need to find the least number of something. Your math might give you x>integer, so the answer would be integer plus 1.

Take a second to understand the answer choices before rushing to select and answer.

Question 14

Objects in the Line

Answer 14

Draw the line. Graph the positions for each scenario clearly and accurately. Be careful with the greater than/less than question. Slow down to confirm what the question is asking.