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yaboi-wyatt-d / Unit 1

September 01, 2025 09:35
algebra
financial math
mathematics
problem solving
word problems
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Unit 1

A concise cheat sheet to tackle various word problems, including financial, statistical, and everyday scenarios. Learn how to identify key information, set up equations, and solve for the unknown.

Financial Word Problems

Earnings & Savings

Hourly Wage:
Earnings = (Wage/Hour) × (Hours/Week) × (Weeks)

Example:
$10.79/hour, 21 hours/week, 18 weeks
Earnings = 10.79 × 21 × 18 = $4,078.62

Simple Interest:
Total Boxes = Total Cost / (Cost / Box)

Example:
$74 interest, $3/box
Boxes = 74 / 3 = 24.66…
Round down to 24 boxes

Sale Savings:
Savings = (Normal Price) - (Sale Price)

Example:
Regular $3.50, Sale 3 for $10
Savings = (3 × 3.50) - 10 = $0.50

Total Revenue:
Revenue = (Quantity) × (Price/Unit)

Example:
174 steers, $2,062.50/steer
Revenue = 174 × 2062.50 = $358,875.00

Cost-Benefit Analysis:
Breakeven Visits = (Annual Cost) / (Cost per visit)

Example:
Annual pass $1,149, Visit cost $113.34
Visits = 1149 / 113.34 ≈ 10.14
Round up to 11 visits

Savings with Kiosk:
Total Saving = (Number of Kiosks) * (Saving Per Kiosk)

Example:
6,454 kiosks, $28,800 saving/year
Saving = 6454 * 28800 = $185,875,200

Payment Calculations

Production Output:
Total Energy = (Energy / Area) × (Area)

Example:
9.5 kWh/sq ft, 500 sq ft
Energy = 9.5 × 500 = 4,750 kWh

Lost income:
(Wage/Hour) * (Hours Lost)

Example:
$15/hour, 54.17 hours
Lost Income = 54.17 * 15 = $812.50

Moving Company Payment:
Total Pay = Base + (Safe Pots * Pay per Pot) - (Damaged Pots * Deduction per Pot)

Example:
Base $150, $1/safe pot, $5 deduction/broken pot
Total = 150 + (574 * 1) - (6 * 5) = $694

Percentage & Fraction Word Problems

Percentage Calculations

Percentage Calculation:
Percentage = (Part ÷ Whole) × 100

Example:
294 women out of 558 athletes
Percentage = (294 / 558) × 100 = 52.7%

Percentage Increase:
% Increase = ((New Value - Old Value) ÷ Old Value) × 100

Example:
1968: 2,614,340 members, 2018: 16,118,169
% increase = ((16,118,169 - 2,614,340) / 2,614,340) × 100 ≈ 517%

Required Quantity:
Required = Total × Percentage

Example:
3,500 seniors, 80% graduation rate
Required grads = 3500 × 0.80 = 2,800

Conversion to Percent:
Percent = Decimal × 100

Example:
Batting average 0.305
Percent = 0.305 * 100 = 30.5%

Accuracy Percentage:
Accuracy % = (Successes ÷ Attempts) × 100

Example:
29 goals out of 115 shots
Accuracy = (29/115) × 100 = 25.2%

Winning Percentage:
Win % = (Wins ÷ Total Games) × 100

Example:
72 wins out of 82 games
Win = (72/82) × 100 = 87.8%

Fraction Calculations

Fraction of Population:
Fraction = (Part) ÷ (Whole)

Example:
80.7 million out of 7.2 billion
Fraction = 80.7M / 7.2B = 269/24000

Finding the Total:
Total = Known Value ÷ Known Fraction

Example:
200 homes = 20% of energy
Total homes = 200 / 0.20 = 1000

Combined Fractions:
Food fraction = (1/3) * (1/2)

Example:
1/3 budget on housing, 1/2 of that on food
Food Fraction = (1/3) * (1/2) = 1/6

Fraction of Total:
Fraction = Total Educated ÷ Total People

Example:
99/100 + 162/180. Total educated 261/280

Estimating Total:
Total Population = Known Population/Known Fraction

Example:
NY Muslim population 770770 equals 1/4 of America’s Muslim population
Total population = 770770 / (1/4) = 3,083,080

Fraction of Recipe:
New Amount = Fraction of recipe * Recipe Yield

Example:
Recipe: 2½ cups flour → 48 cookies. You have 2 cups
Cookies = 48 * (2/2.5) = 38 cookies

Conversion & Rate Word Problems

Unit Conversion

Distance Conversion:
Total Blocks = Total Miles / Miles per Block

Example:
8 miles, 0.11 miles/block
Blocks = 8 / 0.11 = 72.73 blocks

Weight Conversion:
Total Ounces = Total Pounds * 16 Ounces per Pound

Example:
Recipe: 1.5 lb chicken with 7oz pieces
Pieces = (1.5*16) / 7 = 4 pieces

Calculating Gallons from Ounces:
Gallons = Total Ounces / 128 Ounces per Gallon

Example:
10 six-packs of 12oz cans gives 720oz
Gallons = 720/128 = 5.63 gallons

Calculating Miles per Hour:
Speed = Distance (miles) / Time (hours)

Example:
Marathon distance 26.2 miles in 2.133 hours
Speed = 26.2 / 2.133 = 12.281 mph

Pounds per Gallon:
Pounds per gallon = Total Pounds / Gallons

Example:
Gigi the Cow produced 75,000 lbs of milk = 8,700 gallons
Pounds per gallon = 75000/8700 = 8.6 lb/gal

Rates and Ratios

Annual Panels:
Homes = Total Homes * (Homes Powered with Panels / Total Panels)

Example:
Total Panels power 200 homes or 20% of the total
Total homes that can be powered with 100% of panels = 200/0.2 = 1000

Annual Panels:
Required = Total Shots * Accuracy

Example:
15 shots, average 0.433
Minimum makes to reach average = 15*0.433 = 7 shots

Calculating Yearly Percentage:
Injury Range = Annualy Injured * ( Injury Percentage Range )

Example:
1/3 fall, injury range 20-30%
% of 65+ suffer moderate/severe injury annually = (1/3)*(20-30)% = 6.66%

Determining Power Consumption Cost:
Energy Use (kWh) = (Wattage / 1000) * Hours Used
Cost = Energy Use * Rate per kWh

Example:
1,875-watt hair dryer for 15 minutes/day, rate = $0.0860 per kWh
Cost = (1.875*0.25)*0.0860= $0.0403/day

Calculating Megapixels for Print:
Total Pixels = (Width * DPI) * (Height * DPI)
Megapixels = Total Pixels / 1,000,000

Example:
Print an 11″×14″ photo at 300 dpi
Megapixels = (11300)(14*300) / 1000000 = 13.9 MP

Time and Percentage Change Calculations

Time Calculations

Marathon Time Decrease:
Time Decrease = Original Time - New Time
% Decrease = (Time Decrease / Original Time) × 100

Example:
Fastest marathon time fell from 2:08:16 (1990) to 2:04:15 (2012)
% decrease = ((2.1378 - 2.0708) / 2.1378) × 100 ≈ 3.13%

Adjust Recipe Based on Quantity

Adjusting a Recipe:
New Amount = Fraction of recipe * Recipe Yield

Example:
Recipe: 2½ cups flour → 48 cookies. You have 2 cups
Cookies = 48 * (2/2.5) = 38 cookies

Find Value After Change

Finding the Original Value:
Original = 31,667 / 1.92 ≈ 16,493 students

Example:
Original = Value at present / (1 + Change percentage )