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.
Half-Life Problem: Exponential Decay

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

Locker Problem: Perfect Squares Logic

Classic logic puzzle: which lockers are open after 100 days of toggling? Discover the perfect square connection.

Recursive Formula: Decreasing Sequence

Write a recursive formula for newsletter subscriptions decreasing by 80 per month, starting at 4,000.

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.

Robot Motion: Find When It Returns Home (Cubic Roots)

Robot distance: d(t) = t³−13t²+40t. Find all times t when d(t)=0 (returned home). Solve cubic polynomial.

Savings Account: Geometric Sequence Formula

Bailee deposits $500 with balance multiplying by 1.0025 monthly. Write the explicit formula for amount after n months.

Systems of Equations: Photo Contest Problem

38 bird photos, 200 points total. Songbirds worth 4 pts each, birds of prey 20 pts. Find how many of each type.

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.