CEUET Mathematics — Word Problems — Number, Age, Work, Motion, Mixture, InvestmentSummary
Word Problems — Number, Age, Work, Motion, Mixture, Investment is one of the highest-yield Mathematics topics for the CEUET. Centro Escolar University has included questions from this chapter in every recent CEUET 2026 cycle, so understanding the core ideas and common traps is essential for improving your mock score. This summary walks through what Word Problems — Number, Age, Work, Motion, Mixture, Investment is about, the big concepts, the formulas that matter, and how CEUET frames questions on this topic.
Exam context
On the CEUET 2026, the Mathematics subtest carries a "Core" weight in Centro Escolar University's pattern. Word Problems — Number, Age, Work, Motion, Mixture, Investment lands at position 4th out of 9 in the standard review order. Target score is Competitive overall score, and roughly a meaningful share of items come from Mathematics on a typical CEUET paper.
Word Problems — Number, Age, Work, Motion, Mixture, Investment - Summary
Word problems in mathematics require translating real-world situations into mathematical expressions and equations. This chapter covers six major types of word problems commonly appearing in Philippine college entrance exams: number problems, age problems, work problems, motion problems, mixture problems, and investment problems. Each type follows specific patterns and solution strategies that, once mastered, make problem-solving systematic and efficient. The key to success lies in understanding the 3 R's and ESP method: Read, Represent, Relate, Equate, Solve, and Prove.
Key Concepts
Converting English phrases into mathematical symbols is fundamental. Key translations include: 'more than' becomes addition (+), 'less than' becomes subtraction (-) with numbers switched, 'times' or 'of' becomes multiplication (×), 'per' or 'divided by' becomes division (÷), and 'is' or 'equals' becomes the equals sign (=). For example, '4 less than twice a number' translates to 2x - 4.
Concept
Translation of Phrases to Mathematical Expressions
Importance
This skill forms the foundation for all word problems, as accurate translation determines whether the solution will be correct.
Number problems involve finding unknown numbers based on given relationships. Consecutive integers differ by 1 (like 5, 6, 7), while consecutive odd or even integers differ by 2 (like 3, 5, 7 or 4, 6, 8). If x is the first integer, consecutive integers are x, x+1, x+2, etc., while consecutive odd/even integers are x, x+2, x+4, etc.
Concept
Number Problems and Consecutive Integers
Importance
These problems teach systematic variable representation and equation setup, skills essential for more complex algebraic problems.
Age problems involve relationships between people's ages at different time periods. Use tables to organize present ages, past ages, and future ages. Remember that everyone ages at the same rate - if 2 years pass, everyone becomes 2 years older. Set up equations based on the given relationships between ages in specific time periods.
Concept
Age Problems with Time Relationships
Importance
Age problems develop logical thinking about time relationships and systematic organization of multiple variables.
Work problems use the principle that Work = Rate × Time. If someone completes a job in x hours, their rate is 1/x of the job per hour. When people work together, add their individual rates to get the combined rate. For example, if Charlie paints a room in 6 hours (rate = 1/6 room/hour) and Donna in 3 hours (rate = 1/3 room/hour), together they work at (1/6 + 1/3) = 1/2 room/hour.
Concept
Work Problems and Combined Rates
Importance
Work problems teach fractional thinking and the concept of rates, applicable in real-world efficiency and productivity calculations.
Motion problems rely on the formula Distance = Rate × Time (D = rt). Use tables to organize the distance, rate, and time for each moving object. The relationship between distances depends on direction: objects moving toward each other have distances that add up to the total distance, while objects traveling in the same direction have equal distances when one overtakes the other.
Concept
Motion Problems Using Distance-Rate-Time
Importance
Motion problems develop spatial reasoning and understanding of relative motion, concepts used in physics and real-world travel calculations.
Mixture problems involve combining solutions with different concentrations. A solution's concentration is the percentage of solute (dissolved substance) in the total volume. Use the formula: Amount of solute = Concentration × Total volume. When mixing solutions, the total amount of solute equals the sum of solutes from individual solutions, and the final concentration equals total solute divided by total volume.
Concept
Mixture Problems and Concentration
Importance
Mixture problems teach percentage calculations and proportional reasoning, essential for chemistry, cooking, and business applications.
Investment problems use the formula Interest = Principal × Rate × Time (I = PRT). For simple interest, interest is calculated only on the original principal. For compound interest, interest is calculated on the principal plus previously earned interest. When solving investment problems, set up equations based on relationships between different investments' returns.
Concept
Investment Problems and Interest Calculations
Importance
Investment problems develop financial literacy and understanding of how money grows over time, crucial life skills for personal finance management.
Important Points
- Always follow the 3 R's and ESP method: Read thoroughly, Represent unknowns with variables, Relate variables through given information, Equate using problem facts, Solve the equation, and Prove by checking the answer
- Pay careful attention to phrase translations - 'less than' and 'subtracted from' require switching the order of numbers in the mathematical expression
- For consecutive integer problems, remember that consecutive integers differ by 1, while consecutive odd or even integers differ by 2
- In age problems, create tables showing ages at different time periods and remember that everyone ages at the same rate
- Work problems require understanding that rates add when people work together, and the combined rate equals 1 divided by the time to complete the job together
- Motion problems depend on whether objects are moving toward each other (distances add) or in the same direction (distances equal when one catches up)
- Mixture problems require careful tracking of both the amount of solution and the amount of pure solute in each component
- Investment problems may involve simple interest (calculated on principal only) or compound interest (calculated on principal plus accumulated interest)
- Always verify answers by substituting back into the original problem statement to ensure the solution makes logical sense
- Use tables and organized layouts to keep track of multiple variables and relationships in complex problems
Chapter Objectives
- Master the 3 R's and ESP problem-solving strategy for all word problem types
- Translate English phrases into mathematical expressions and equations accurately
- Solve number problems including consecutive integers and digit problems
- Apply algebraic methods to age problems involving past, present, and future relationships
- Calculate combined work rates and completion times for work problems
- Analyze motion problems using distance-rate-time relationships
- Solve mixture and concentration problems using percentage calculations
- Compute simple and compound interest in investment problems
Concept Relationships
- All word problem types share the same fundamental approach: translation of English to mathematics followed by algebraic solution
- Number problems form the foundation for understanding variable representation used in all other problem types
- Age problems extend number problems by introducing time as an additional dimension affecting all variables equally
- Work problems apply rate concepts that are also fundamental to motion problems, both using the relationship between quantity, rate, and time
- Mixture problems combine percentage calculations with algebraic thinking, similar to investment problems dealing with rates and returns
- Motion problems and work problems both use tables to organize rate, time, and total quantity information
- Investment problems apply the same percentage thinking used in mixture problems but focus on financial growth over time
- The proof step in all problem types reinforces mathematical reasoning and verification skills essential for exam success
Practical Applications
- Number and digit problems develop pattern recognition skills useful in computer programming and mathematical sequences
- Age problems teach logical reasoning about time relationships, applicable in planning, scheduling, and historical analysis
- Work problems help calculate project completion times, workforce efficiency, and resource allocation in business and engineering
- Motion problems solve real-world travel planning, meeting point calculations, and transportation logistics
- Mixture problems apply to cooking recipes, chemical formulations, medicine dosages, and manufacturing processes
- Investment problems provide essential financial literacy for personal savings, loan calculations, retirement planning, and business finance decisions
- The systematic problem-solving approach transfers to scientific method, engineering design, and analytical thinking in any field
- Translation skills between verbal and mathematical language enhance communication and critical thinking abilities
In summary
Word problems in mathematics are essentially translation exercises that convert real-world situations into mathematical language. Success depends on mastering the systematic 3 R's and ESP approach: Read carefully, Represent unknowns with variables, Relate variables through given information, Equate using problem facts, Solve algebraically, and Prove by verification. Each problem type—number, age, work, motion, mixture, and investment—has specific patterns and formulas, but all share the same fundamental solution strategy. Regular practice with these problem types develops not only mathematical skills but also logical reasoning and analytical thinking abilities essential for academic and professional success. The key is to approach each problem methodically, organize information clearly using tables when helpful, and always verify that the final answer makes sense in the context of the original problem.
Next steps
After mastering this chapter, students should practice mixed problem sets that combine different word problem types to develop flexibility in problem recognition and solution approaches. Focus on identifying problem types quickly, setting up equations accurately, and developing speed in algebraic manipulation. Advanced students can explore optimization problems, systems of equations arising from multiple constraints, and word problems involving quadratic equations. Regular practice with past UPCAT, ACET, and other entrance exam questions will help develop test-taking strategies and time management skills essential for exam success.
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Algebra — Sets, Exponents, Radicals, Polynomials & Equations
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Geometry — Lines, Angles, Polygons, Triangles & Circles
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