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.Find when two health club costs are equal using a system of linear equations. Substitution or graphing method.
Salma sold 60 cups totaling 920 ounces. Small=12oz, large=16oz. Find cups of each size using systems.
Classic logic puzzle: which lockers are open after 100 days of toggling? Discover the perfect square connection.
Given 45 m² of material for a square-base box with no top, find dimensions that maximize volume. Uses calculus and constraints.
1120 m fencing, one side is a river (unfenced). Find dimensions to maximize rectangular plot area.
Write a recursive formula for newsletter subscriptions decreasing by 80 per month, starting at 4,000.
Write a revenue equation and find the price that maximizes amusement park admission revenue.
Fatoumata's rewards card problem. Write and solve a linear inequality to find the minimum visits needed for a free movie ticket.
Robot distance: d(t) = t³−13t²+40t. Find all times t when d(t)=0 (returned home). Solve cubic polynomial.
Find the probability that two competitors throw the same choice in rock-paper-scissors. Express as a fraction.