Algebra Word Problem Solver

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.

Formula

d = r × t | Work: 1/A + 1/B = 1/T | Mixture: C₁V₁ + C₂V₂ = C_f(V₁+V₂)

d = r × t
distance = rate × time (distance-rate-time problems)
1/A + 1/B = 1/T
combined work rate: A and B working together to finish in time T
C₁V₁ + C₂V₂
mixture: concentration × volume for each solution being combined

Word Problem Solver

Select a problem type and enter the values.

Word Problem Formula Reference

Problem TypeKey FormulaVariable SetupCheck
Distance/Rate/Timed = r × tLet t = time; rates × times = distancesSum of distances = total
Work/Rate1/A + 1/B = 1/TA, B = individual times; T = togetherT < min(A, B)
MixtureC₁V₁ + C₂V₂ = Cf(V₁+V₂)Let x = volume of first solutionFinal concentration between C₁ and C₂
Consecutive intsn + (n+1) + (n+2) = sumn = first integerVerify sum
Consecutive even/oddn + (n+2) + (n+4) = sumn = first even/oddAll must be even or all odd
Age (current)Express relative to xLet x = one person's ageAll ages positive
Age (future)Add years to each ageWrite condition for future agesVerify in original
Coin/MoneyValue × Count = AmountLet x = count of one coin typeSum of counts = total coins

Disclaimer

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.

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