💡 What You Will Learn
On the GED, word problems ask you to translate English sentences into algebraic equations. Once you know which words signal which operation, every word equation becomes straightforward. This lesson builds that skill step by step!
Every word problem is hiding an algebraic equation. Your job is to read the words, find the unknown value (call it x), write the equation, and solve for x.
The thing you're trying to find is x. It could be a price, a count, a distance — anything unknown.
"More than" → + | "Less than" → − | "Times" → × | "Split equally" → ÷
Once you have the equation, use inverse operations to isolate x — just like one-step and two-step equations!
"Miguel and 3 friends split the bill. Each person paid $13. What was the total?"
x ÷ 4 = 13
x is the total. Split by 4 people = $13 each.
The GED doesn't ask you to solve the equation — it asks you to identify the correct equation from four choices. If you can translate the words to math, you'll get it right every time!
| Operation | Symbol | Key Words to Watch For |
|---|---|---|
| Addition | + | more than, increased by, added to, total, sum, received, gained, combined |
| Subtraction | − | less than, decreased by, fewer, difference, lost, spent, left over, remaining |
| Multiplication | × | times, multiplied by, of, at __ each, per, product, groups of |
| Division | ÷ | split equally, divided by, per person, shared, ratio, quotient, each |
| Equals | = | is, are, was, gives, results in, totals, costs, makes, equals |
| Unknown (x) | x | how many, how much, what is, find, unknown, missing, ? |
"5 less than x" → x − 5 (NOT 5 − x)
The order matters! "A less than B" always means B − A.
🔑 Memory Tip
Circle the key words in the problem first. Then match each word to its symbol. Finally, put the numbers and x in the right positions. The equation will write itself!
Make sure the numbers go in the RIGHT positions!
"Carlos needs $135, has $78" → x + 78 = 135 ✅
NOT: x + 135 = 78 ❌ (that would give a negative answer!)
Something happens at a rate: price × quantity, speed × time, groups × size → equals a total.
A total is shared or split among a group → each person/item gets an equal portion.
First read for the story. Second read to find: What is the unknown? What numbers are given? What operation is described?
Write out loud what x represents. "x = the number of bags" or "x = the total cost." This prevents mistakes!
Circle the operation words. Build the equation using the numbers, x, and the operation symbol. Check: does the equation match the story?
Plug your answer back into the word problem. If you found x = 5 packs, does $8 × 5 = $40? ✅ If not, recheck your equation.
| Situation | Equation Pattern | Example |
|---|---|---|
| Started with + received | start + x = total | 29 + x = 41 |
| A more than B = C | x + A = C | x + 30 = 47 |
| Price × quantity = total | Px = total | 8x = 40 |
| Total split among N | x ÷ N = each | x ÷ 4 = 13 |
| Need − have = still need | x + have = need | x + 78 = 135 |