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.Initial collection $5. Each person adds same amount. Find total after the 35th person contributes.
Count ways to assign 12 astronauts to two rockets (3 and 4 people) with 4 experienced required. Combinatorics with constraints.
Find number of ways to select 5 starters from 12 players using combinations. C(12,5) formula.
Compare two phone plans: 25¢/min vs. $0.95 + 12¢/min. Find when the second plan becomes preferable.
Minimize bus rental cost for 400 students with capacity and driver constraints. Linear programming word problem with practical application.
Find probability of selecting all Republicans from a mixed group. Master combination counting.
Solve half-life exponential decay: find time for water to drop 50% using decay formula. Multiple methods.
Solve a classic two-variable system: farm animals with known totals and leg counts. Master substitution and elimination methods.
Extend the Fibonacci sequence for daisy petals: 13, 21, 34, ?, ?
Find the greatest common divisor to determine how many equal events can be held with students from two schools.