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3.4 Decimal Word Problems & Financial Calculations

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ACCUPLACER Arithmetic Exam

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1 Chapter 1: Whole Number Operations

1.1 Basic Whole Number Arithmetic 1.2 Order of Operations & Grouping Symbols 1.3 Number Properties, Factors & Prime Factorization 1.4 Whole Number Estimation, Rounding & Applied Word Problems

2 Chapter 2: Fraction Operations

2.1 Fraction Fundamentals & Simplifying 2.2 Addition & Subtraction of Fractions and Mixed Numbers 2.3 Multiplication & Division of Fractions and Mixed Numbers 2.4 Real-World Fraction Applications & Word Problems

3 Chapter 3: Decimal Operations

3.1 Decimal Place Value, Rounding & Comparing Decimals 3.2 Addition & Subtraction of Decimals 3.3 Multiplication & Division of Decimals 3.4 Decimal Word Problems & Financial Calculations

4 Chapter 4: Percent

4.1 Percent Concepts & Conversions 4.2 Percent of a Quantity & Percent Equations 4.3 Percent Increase, Decrease & Percent Change 4.4 Practical Percent Applications

5 Chapter 5: Number Comparisons & Equivalents

5.1 Ordering Mixed Numerical Forms 5.2 Equivalent Numerical Representations & Conversion Strategies 5.3 Ratios, Unit Rates & Proportional Reasoning

3.4 Decimal Word Problems & Financial Calculations

Key Takeaways Explain This Topic AI

Unit price equals total cost divided by quantity (Unit Price = Total Cost / Quantity); comparing unit prices identifies the best value regardless of package size.

Total purchase cost equals the sum of individual item subtotals (Quantity x Unit Price); cash change due equals amount tendered minus total purchase cost.

Gross paycheck earnings equal regular wage pay (up to 40 hours) plus overtime pay (1.5 x hourly wage x hours over 40); net pay equals gross pay minus itemized decimal deductions.

Multi-step decimal word problems require systematic step-by-step calculation pathways while preserving exact decimal precision throughout intermediate steps.

In financial calculations, maintain precision to at least 3-4 decimal places during intermediate steps and round to the nearest cent ($0.01) only at the final step.

Last updated: August 2026

3.4 Decimal Word Problems & Financial Calculations

Real-world applications of arithmetic frequently involve decimal numbers, particularly in context of money, wage calculations, unit pricing, and scientific or technical measurements. Word problems on the ACCUPLACER Arithmetic exam assess your ability to translate verbal scenarios into multi-step mathematical operations while executing decimal arithmetic with absolute precision.

Unit Pricing and Best-Buy Comparisons

When purchasing goods sold in different package sizes and prices, consumers compare unit prices to determine which option offers the best financial value.

The Unit Price Formula

Unit Price = Total Price or Cost Quantity (ounces, pounds, items) \text{Unit Price} = \frac{\text{Total Price or Cost}}{\text{Quantity (ounces, pounds, items)}} Unit Price = Quantity (ounces, pounds, items) Total Price or Cost ​

Comparative Unit Price Table

Consider comparing three options for purchasing olive oil:

Option Package Size Total Price Unit Price Calculation Unit Price per Ounce Best Value Rank

Brand A 12 oz bottle $4.20 $ 4.20 12 \frac{\text{\textdollar}4.20}{12} 12 $ 4.20 ​ 0.35 0.35 0.35 / oz 3rd (Most Expensive)

Brand B 20 oz bottle $6.40 $ 6.40 20 \frac{\text{\textdollar}6.40}{20} 20 $ 6.40 ​ 0.32 0.32 0.32 / oz 2nd

Brand C 32 oz bottle $8.96 $ 8.96 32 \frac{\text{\textdollar}8.96}{32} 32 $ 8.96 ​ 0.28 0.28 0.28 / oz 1st (Best Buy)

Step-by-Step Worked Example: Best-Buy Analysis

A grocery store sells Brand A peanut butter in a 16-ounce jar for $4.32 and Brand B peanut butter in a 24-ounce jar for $6.00 . Which brand is the better buy, and by how much per ounce?

Step 1: Calculate Unit Price for Brand A: Unit Price A = $ 4.32 16 = $ 0.27 per ounce \text{Unit Price}_A = \frac{\$4.32}{16} = \mathbf{\$0.27 \text{ per ounce}} Unit Price A ​ = 16 $4.32 ​ = $0.27 per ounce

Step 2: Calculate Unit Price for Brand B: Unit Price B = $ 6.00 24 = $ 0.25 per ounce \text{Unit Price}_B = \frac{\$6.00}{24} = \mathbf{\$0.25 \text{ per ounce}} Unit Price B ​ = 24 $6.00 ​ = $0.25 per ounce

Step 3: Compare Unit Prices and calculate savings: $ 0.27 − $ 0.25 = $ 0.02 per ounce \$0.27 - \$0.25 = \mathbf{\$0.02 \text{ per ounce}} $0.27 − $0.25 = $0.02 per ounce

Conclusion: Brand B is the better buy by $0.02 per ounce .

Total Purchase Cost, Subtotals & Cash Change

Retail transactions involve multiplying quantities by unit prices, summing subtotals, and determining cash change returned from tendered cash payments.

General Financial Transaction Procedure

Itemized Subtotals: Multiply quantity by item price for each line item.

Total Cost: Sum all itemized subtotals.

Change Returned: Subtract Total Purchase Cost from Amount Tendered (Cash Paid).

Step-by-Step Worked Example: Multi-Item Register Transaction

David purchases 3 notebooks at $2.85 each , 4 gel pens at $1.45 each , and 1 desk lamp for $18.95 . If he pays with a $50 bill , how much change should he receive?

Step 1: Calculate line item subtotals:

Notebooks: 3 × $ 2.85 = $ 8.55 3 \times \text{\textdollar}2.85 = \mathbf{\text{\textdollar}8.55} 3 × $ 2.85 = $ 8.55

Gel pens: 4 × $ 1.45 = $ 5.80 4 \times \text{\textdollar}1.45 = \mathbf{\text{\textdollar}5.80} 4 × $ 1.45 = $ 5.80

Desk lamp: 1 × $ 18.95 = $ 18.95 1 \times \text{\textdollar}18.95 = \mathbf{\text{\textdollar}18.95} 1 × $ 18.95 = $ 18.95

  • Step 2: Calculate Total Purchase Cost: 8.55 5.80 + 18.95 33.30 ( Total Cost ) \begin{array}{rl}
  • 8.55 \\
  • 5.80 \\
  • + 18.95 \\
  • \hline
  • \mathbf{33.30} & (\text{Total Cost})
  • \end{array} 8.55 5.80 + 18.95 33.30 ​ ( Total Cost ) ​ ​
  • Step 3: Calculate Change Due from $50.00: 50.00 − 33.30 16.70 ( Change Due ) \begin{array}{rl}
  • 50.00 \\
  • 33.30 \\
  • \hline
  • \mathbf{16.70} & (\text{Change Due})
  • \end{array} 50.00 − 33.30 16.70 ​ ( Change Due ) ​ ​

Final Answer: David receives $16.70 in change.

Wage and Paycheck Mathematics

Calculating gross pay involves computing regular hourly wages and overtime pay. Overtime is typically paid at "time-and-a-half" ( 1.5 × regular hourly wage 1.5 \times \text{regular hourly wage} 1.5 × regular hourly wage ) for all hours worked beyond 40 hours per week.

Key Paycheck Formulas

Regular Pay = Regular Hours (up to 40) × Hourly Rate \text{Regular Hours (up to 40)} \times \text{Hourly Rate} Regular Hours (up to 40) × Hourly Rate

Overtime Rate = 1.5 × Hourly Rate 1.5 \times \text{Hourly Rate} 1.5 × Hourly Rate

Overtime Pay = Overtime Hours (hours over 40) × Overtime Rate \text{Overtime Hours (hours over 40)} \times \text{Overtime Rate} Overtime Hours (hours over 40) × Overtime Rate

Gross Pay = Regular Pay + Overtime Pay \text{Regular Pay} + \text{Overtime Pay} Regular Pay + Overtime Pay

Net Pay (Take-Home Pay) = Gross Pay − Total Deductions \text{Gross Pay} - \text{Total Deductions} Gross Pay − Total Deductions

Step-by-Step Worked Paycheck Example

Samantha earns $18.50 per hour as a dental technician. Last week she worked 46 hours . Her mandatory payroll deductions (tax, insurance, retirement) totaled $142.80 . What was Samantha's net pay for the week?

Step 1: Determine regular and overtime hours:

  • Regular hours = 40
  • Overtime hours = 46 − 40 = 6 46 - 40 = \mathbf{6} 46 − 40 = 6

Step 2: Compute Regular Pay: Regular Pay = 40 × $ 18.50 = $ 740.00 \text{Regular Pay} = 40 \times \$18.50 = \mathbf{\$740.00} Regular Pay = 40 × $18.50 = $740.00

Step 3: Compute Overtime Rate and Overtime Pay:

Overtime Rate = 1.5 × $ 18.50 = $ 27.75 per hour 1.5 \times \text{\textdollar}18.50 = \mathbf{\text{\textdollar}27.75 \text{ per hour}} 1.5 × $ 18.50 = $ 27.75 per hour

Overtime Pay = 6 × $ 27.75 = $ 166.50 6 \times \text{\textdollar}27.75 = \mathbf{\text{\textdollar}166.50} 6 × $ 27.75 = $ 166.50

Step 4: Compute Gross Pay: Gross Pay = $ 740.00 + $ 166.50 = $ 906.50 \text{Gross Pay} = \$740.00 + \$166.50 = \mathbf{\$906.50} Gross Pay = $740.00 + $166.50 = $906.50

Step 5: Compute Net Pay: Net Pay = $ 906.50 − $ 142.80 = $ 763.70 \text{Net Pay} = \$906.50 - \$142.80 = \mathbf{\$763.70} Net Pay = $906.50 − $142.80 = $763.70

Final Answer: Samantha's net pay is $763.70 .

Multi-Step Utility & Fuel Efficiency Applications

Decimal word problems frequently combine division and multiplication in practical physical applications, such as calculating automobile fuel economy and travel costs.

Worked Example: Fuel Efficiency and Travel Cost

A driver traveled 418.5 miles on a single tank of gasoline, consuming 13.5 gallons of fuel. Gasoline costs $3.60 per gallon .

What was the vehicle's fuel efficiency in miles per gallon (MPG)?

What was the total cost of the fuel consumed on this trip?

Part 1: Calculate Fuel Efficiency (MPG): MPG = Miles Driven Gallons Consumed = 418.5 13.5 \text{MPG} = \frac{\text{Miles Driven}}{\text{Gallons Consumed}} = \frac{418.5}{13.5} MPG = Gallons Consumed Miles Driven ​ = 13.5 418.5 ​

Shift decimal 1 place right: 4185 ÷ 135 = 31 MPG 4185 \div 135 = \mathbf{31 \text{ MPG}} 4185 ÷ 135 = 31 MPG

Part 2: Calculate Total Fuel Cost: Total Cost = 13.5 gallons × $ 3.60 / gallon = $ 48.60 \text{Total Cost} = 13.5 \text{ gallons} \times \$3.60 / \text{gallon} = \mathbf{\$48.60} Total Cost = 13.5 gallons × $3.60/ gallon = $48.60

Final Answers: 31 MPG and $48.60 total fuel cost.

ACCUPLACER Exam Traps & Common Errors

Warning

Trap 1: Inverted Unit Price Division Dividing quantity by price (e.g., 16 / $ 4.32 = 3.70 16 / \text{\textdollar}4.32 = 3.70 16/ $ 4.32 = 3.70 ounces per dollar) instead of price by quantity ( $ 4.32 / 16 = $ 0.27 \text{\textdollar}4.32 / 16 = \text{\textdollar}0.27 $ 4.32/16 = $ 0.27 per ounce) is a classic trap. Unit price always has money in the numerator.

Warning

Trap 2: Forgetting the 1.5 Overtime Multiplier Calculating all 46 hours at the regular $18.50 rate ( 46 × 18.50 = $ 851.00 46 \times 18.50 = \text{\textdollar}851.00 46 × 18.50 = $ 851.00 ) forgets that hours over 40 earn 1.5 × 1.5 \times 1.5 × wage.

Warning

Trap 3: Premature Rounding in Financial Steps Rounding intermediate quotients to two decimal places early can introduce errors in cents. Maintain exact decimals until the final answer.