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.
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.

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 Fruit Cost

Sally and Steve buy apples and oranges. Write and solve a system of 2 equations to find the price of each fruit.

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.

Round & Rectangular Tables: System Problem

Set up and solve: 25 tables, 190 total seats. Round tables (6 seats), rectangular tables (8 seats). Find quantities.

Three Consecutive Integers Sum 51

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

Three-Legged Race: Catching Up Problem

Solve a system of equations for a race with staggered start. Find when faster runner catches up.