Module 9: General Word Problems

Question 1

Setting up an age matrix

Answer 1

Helpful for solving age problems.

X axis: Characters in problem
Y axis: different timeframes
Values: ages of characters at each timeframe

Question 2

When I am able to translate two or more equations from a word problem, I will

Answer 2

use substitution or elimination to combine them. DON’T mash them all together to the start, this will probably be incorrect

Question 3

Price per Item

Answer 3

Total cost of items purchased / number of items purchased

Question 4

How to calculate profit

Answer 4

Revenue - (Fixed Costs + Variable Costs)

Question 5

“Split the Bill” problems

Answer 5

1) Set up two fractions: the original split of the bill x/y, where X is the total cost and Y is the number of people splitting, and the new split (x/z where Z is the new number of splitters.)
2) If given in the problem add the difference in per-person cost to the equation

x/2 = x/4 + 40 (if told that x/2 is $40 more each)

3) Simplify - multiply entire equation by LCD (4) and go from there

Question 6

Fixed Rate Salary/Fee Comparison

Write a formula: In Job A you earn $10 per hour for the first 20 hours and then $15 per hour for each hour thereafter. In job B you earn $8 per hour for the first 16 hours and then $18 per hour for each hour thereafter. At what number of hours do both jobs pay the same amount?

Answer 6

T = # of hours
Job A: 10(20) + 15(T - 20)
Job B: 8(16) + 18(T - 16)

Set A & B equal to each other and solve for T.

Question 7

When I see a fractional word problem, I will

Answer 7

remember that all fractional parts must sum to a whole. Use this to set up an equation

Question 8

Set up this equation:

“A pilot was required to fly a certain number of hours one day. In the morning, she flew 1/4 of the day’s required hours plus 2 more. In the afternoon, she flew 2/5 of the day’s remaining required hours. Then in the evening, she flew the 4 remaining hours.”

Answer 8

Make H = total hours in the day.

1) The morning: subtract the portion she flew from the original sum
* * H - (1/4H + 2) **

2) The afternoon: take the equation from the morning, multiply it by the given proportion, then simplify.
2/5 (H - (1/4H + 2))
2/5 (4/4H - (1/4H + 2))
2/5 (4/4H - 1/4H - 2)
2/5 (3/4H - 2/1)
6/20H - 4/5
** 3/10H - 8/10 **

3) The evening: they give you the raw number which is nice. Set steps 1, 2 & 3 equal to H. (The final step would be to solve.)
NOTE: DON’T include “H -“ from step 1.

(1/4H + 2) + (3/10H - 8/10) + 4 = H

Question 9

Types of interest problems (2)

Answer 9

Simple interest: Based on the original amount of principal borrowed/lent

Compound interest: amount earned/paid builds on new interest that accumulates

Question 10

Simple Interest formula

Answer 10

Principal x Rate x Time

Principal: initial amount of $
Rate: expressed as a decimal or fraction
Time: in units relative to the given rate. Be careful with the time - if interest is annual but 8 months have passed, the time would be 8/12

Question 11

Compound Interest formula

Answer 11

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

A = future value
P = initial value (principal)
r = interest rate
t = time (usually in years)
n = number of compounding periods per year

Question 12

Linear Growth Formula

Answer 12

F = kn + p

F: final value after growth

k: growth constant
n: number of growth periods
p: original value

Manipulate the above formula algebraically to solve growth problems.

Question 13

The sum of five consecutive integers can be expressed as

Answer 13

x + (x + 1) + (x + 2) + (x + 3) + (x + 4)

OR

5x + 10

Question 14

When I see a mixture problem, I will

Answer 14

create a matrix

Question 15

Dry Mixture formula

Answer 15

X * Y = amount, as in

Price * Volume
Interest rate * Value
Relevant Fraction * Total Group

Question 16

When counting the difference between items, I will

Answer 16

Use the counting formula:

Last - First - 1

Question 17

Exponential Growth Formula

Answer 17

xy^z

x = start value
y = the constant factor of growth during each period
z = number of periods

Question 18

Unit Conversions: Guidelines to follow (2)

Answer 18

1) If converting big numbers and it’s an “approximation” problem, use Scientific Notation when possible
2) Use “conversion factors.” Multiply the value to be converted by a ratio expressed as a fraction, where (New unit / Old unit) = 1. Then, cancel out the old unit values when cross multiplying.