Word Problems

Knowing how to solve an equation is only half the battle. Word problems test whether you can build the equation yourself, which is just as just as important as solving.

Click here for some tips on linear equations

Word problems in Algebra 1 fall into a few recognizable patterns: setting up a linear equation from a scenario, writing an inequality with a constraint, building a system of equations, and choosing between a linear and exponential model. The algebra is usually straightforward once the equation is set up correctly.

• Define your variable first — write down what x represents, including units

• "Is" → =, "of" → × for percent problems (e.g. "30 is what % of 120?" → 30 = x · 120)

• "At most," "no more than" → ≤   |   "at least," "no fewer than" → ≥

• Rate problems: distance = rate × time; set up the equation for the unknown

• Two-quantity problems: assign one variable, express the second in terms of it

✓ Always check that your answer makes sense in context. A negative number of hours worked, or a fractional number of people, should make you go back and check your setup — not just your algebra.

Worked example

Take a look at this example below (and delete the lines if you want to try it yourself). If you need more help, click the link below the box.

Problem: Two friends are saving money. Alex has $120 and saves $15 per week. Jordan has $60 and saves $25 per week. After how many weeks will they have the same amount?

Steps:

1. Write an expression for each: Alex = 120 + 15w; Jordan = 60 + 25w.

2. Set them equal

3. Solve

If you found this scratchpad helpful, get our Chrome extension to use it with almost any algebra problem!

Try it yourself! Below is an exam-style problem

Problem: A school is ordering buses for a field trip. Each bus holds 48 students. There are 310 students going on the trip.

(a) Write an inequality to represent the minimum number of buses b needed.(b) Solve the inequality. How many buses must be ordered?(c) If each bus costs $175 to rent, what is the total cost?

Let's get started.

1. Type your next step below the problem

2. Press enter to add a new line of math 

3. Our AI checks your work as you go 🟢means you're on the right track, ❌means something's off.

4. Made a mistake? Use Ctl+Z to undo a line. Right click to see other shortcuts.

Click here to see the answer

STEP-BY-STEP SOLUTION

1. Let b = number of buses needed

2. Write the inequality: 48b ≥ 310

3. Divide both sides by 48: b ≥ 6.458...

4. Since you can't order a fraction of a bus, round up: b = 7 buses

5. Total cost: 7 × $175 = $1,225

For more practice with linear equations, check out these resources:

https://momentofmath.com/mom.html (look under Algebra 1 Real-world problems)