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.
Ticket Sales: System of Equations Problem

Globe Theater sold 400 tickets for $3,100. Adults $9, children $5. Solve system to find each type. Substitution & elimination methods.

Gym Cost Comparison

Two gyms charge different fees. Find when monthly costs are equal. Linear equation problem with multiple methods included.

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.

Maximize Box Volume | Calculus Optimization

Given 45 m² of material for a square-base box with no top, find dimensions that maximize volume. Uses calculus and constraints.

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.

Rock-Paper-Scissors Probability

Find the probability that two competitors throw the same choice in rock-paper-scissors. Express as a fraction.