Algebra Practice Problems

Algebra word problems are the broadest category — any scenario that translates into equations you need to solve. A number is 7 more than twice another number and their sum is 34: find both numbers. A phone plan charges a flat fee plus a per-minute rate: when does it become cheaper than the competitor? These problems span from simple one-variable equations through systems, quadratics, and inequalities. What they all share is the core algebraic skill: reading a situation, assigning variables, writing equations, and solving. If you can do this reliably, every other word problem category becomes easier because the translation step is the hard part — and this is where you practice it most.
Arithmetic Sequence: Collection Fundraiser

Initial collection $5. Each person adds same amount. Find total after the 35th person contributes.

Mars Mission: Astronaut Selection with Constraints

Count ways to assign 12 astronauts to two rockets (3 and 4 people) with 4 experienced required. Combinatorics with constraints.

Basketball Starting Lineup: Combinations Problem

Find number of ways to select 5 starters from 12 players using combinations. C(12,5) formula.

Half-Life Problem: Exponential Decay

Calculate remaining radioactive tin after 50 days using half-life formula with 10-day period.

Revenue Optimization: Price Increase Problem

Write a revenue equation and find the price that maximizes amusement park admission revenue.

Inequality Word Problem: Rewards Points

Fatoumata's rewards card problem. Write and solve a linear inequality to find the minimum visits needed for a free movie ticket.

System of Equations: Volunteer Cleanup Problem

Two groups cleaning bleachers at different rates. Set up, graph, and solve the system to find when they meet.

Three Consecutive Integers Sum 51

Find three consecutive integers that add to 51. Solve using x + (x+1) + (x+2) = 51.

Three-Set Venn Diagram Problem

Use inclusion-exclusion principle with three overlapping sets. Find houses with exactly two amenities.

Venn Diagram Problem: Math & English Classes

150 freshmen: 85 Math, 70 English, 50 both. Use Venn diagram to find exclusive, combined, and excluded counts.