Reviewed by CalcMulti Editorial Team·Last updated: ·← Algebra Hub
Algebra word problems translate real-world situations into equations that can be solved algebraically. The key skill is not the algebra itself — it is reading the problem carefully, identifying the unknown, defining a variable, and writing the equation that models the situation.
This tool provides step-by-step templates for the most common word problem types: distance-rate-time (d = rt), age problems, mixture problems, work problems (combined rate), and consecutive integer problems. Enter your problem values and get the full solution setup with working.
The universal process for any word problem: (1) Read the problem carefully and identify what is being asked. (2) Assign a variable to the unknown quantity (e.g., let x = the number of hours). (3) Express all other quantities in terms of x. (4) Write an equation based on the relationship described. (5) Solve the equation. (6) Check the answer against the original problem — not just mathematically, but whether it makes physical sense.
Common mistake: solving for x and stopping there, without answering the actual question. The problem might ask for the total distance, not just the time. Or it might ask for BOTH numbers when x represents one of them. Always re-read the final question before writing the answer, and always check that the answer satisfies every condition stated in the problem.
d = r × t | Work: 1/A + 1/B = 1/T | Mixture: C₁V₁ + C₂V₂ = C_f(V₁+V₂)
Select a problem type and enter the values.
| Problem Type | Key Formula | Variable Setup | Check |
|---|---|---|---|
| Distance/Rate/Time | d = r × t | Let t = time; rates × times = distances | Sum of distances = total |
| Work/Rate | 1/A + 1/B = 1/T | A, B = individual times; T = together | T < min(A, B) |
| Mixture | C₁V₁ + C₂V₂ = Cf(V₁+V₂) | Let x = volume of first solution | Final concentration between C₁ and C₂ |
| Consecutive ints | n + (n+1) + (n+2) = sum | n = first integer | Verify sum |
| Consecutive even/odd | n + (n+2) + (n+4) = sum | n = first even/odd | All must be even or all odd |
| Age (current) | Express relative to x | Let x = one person's age | All ages positive |
| Age (future) | Add years to each age | Write condition for future ages | Verify in original |
| Coin/Money | Value × Count = Amount | Let x = count of one coin type | Sum of counts = total coins |
This calculator is for educational purposes only and does not constitute professional advice. Results are based on standard mathematical formulas. Always verify critical calculations with a qualified professional before making important decisions.