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Multi-Step Real-World Problems

Turn everyday situations like shopping, paychecks, gas, and budgets into a plan of steps with the four operations, and check that the answer makes sense.

Practice this skill 30 min Multi-step real-world problems Leer en español
Key idea

What you'll learn

Most GED math questions are word problems that take two, three or four steps: find a total, subtract it from what you paid, divide by the number of people, round to whole boxes. In this lesson you will learn:

  • a simple 4-step plan for any word problem;
  • how to translate words like each, per, left, in all into +, -, \times, \div;
  • how to handle money, rates (per hour, miles per gallon, price per pound) and fixed fees;
  • when to round up, round down, or keep decimals;
  • how to work backwards from a final amount to a starting amount;
  • how to compare two options (which plan or package is cheaper).

Why it matters on the GED: multi-step problems with whole numbers, fractions and decimals are everywhere on the test, and each step is a place to slip. A clear plan, written step by step, is what turns "I know the math" into points.

In real life: this is exactly the math of a paycheck, a grocery bill, a road trip budget or a flooring estimate.

Words to know

  • Total / in all / altogether / combined — usually add (or multiply equal groups): 3 shirts at $12 each cost 3 \times 12 = \$36 in all.
  • Difference / left / remaining / change / how much more — usually subtract: $50 − $36 = $14 change.
  • Each / per / for every — signals a rate; multiply to get a total or divide to get the rate: $45 for 3 hours is $15 per hour.
  • Split equally / shared / average — divide: $72 shared by 6 people is $12 each.
  • Rate — a comparison of two different units: 28 miles per gallon, $3.60 per gallon.
  • Unit price — price for one unit: $5.76 for 24 bottles is \$5.76 \div 24 = \$0.24 per bottle.
  • Fixed fee (flat fee) — a one-time charge that does not depend on how much you use: a $75 service call.
  • Estimate — a rounded, quick answer used to check reasonableness: \$3.459 \times 12.6 \approx \$3.50 \times 13 = \$45.50.
  • Work backwards — start from the final result and undo each step in reverse order.

All Math words in the glossary

1. A 4-step plan for every word problem

1. Understand. Read the question twice. Underline what is being asked ("how much change", "how many boxes", "cost per person"). Circle the numbers you need — some numbers may be extra information.

2. Plan. Decide the steps in order, in words, before calculating. For example: "find the cost of the cheese, find the cost of the apples, add them, subtract from $50."

3. Solve. Do one step at a time and label each result with its unit ($, gallons, hours). Keep full decimals until the end.

4. Check. Does the answer answer the question that was asked? Is it reasonable (estimate)? Can you plug it back in?

Flowchart of the 4-step plan: 1 Understand (what is asked?), 2 Plan (steps in words), 3 Solve (one step at a time, label units), 4 Check (is it reasonable? plug it in). A dashed arrow from Check back to Understand says: if the check fails, go back and re-read.4-step plan for any word problem1 UnderstandWhat is asked?2 PlanSteps in words3 SolveOne step, one unit4 CheckReasonable? Plug inIf the check fails, go back and re-read

Translating words into operations

Words in the problemOperationExample
total, sum, in all, combined, increased by+43.50 + 8.50
difference, left, remaining, change, fewer, decreased by-50 − 21.55
each, per, times, of (with fractions), for every\times3 × $14.50
split, shared equally, per (to find a rate), how many fit\div$72 ÷ 6

Words are clues, not rules. "Per" can mean multiply ($15 per hour for 8 hours → 15 \times 8) or divide ($120 for 8 hours → 120 \div 8 dollars per hour). Always ask: am I finding a total or finding a rate?

2. Money, rates and the GED formula sheet

Two formulas from the GED formula sheet do most of the work in real-world problems:

  • Total cost = (number of units) × (price per unit)
  • Distance = rate × time

Chains of rates. Many problems link two rates. A road trip: miles ÷ (miles per gallon) = gallons; gallons × (price per gallon) = cost.

245\text{ mi} \div 35\tfrac{\text{mi}}{\text{gal}} = 7\text{ gal} \qquad 7\text{ gal} \times \$3.80 = \$26.60

Paychecks. Pay = hourly rate × hours. With mixed numbers, convert first: 6\tfrac{3}{4}\text{ h} = 6.75\text{ h} (since \tfrac{3}{4} = 0.75, not 0.34).

Fixed fee + rate. A plumber charges a $75 call fee plus $45 per hour. For h hours: \text{cost} = 75 + 45h. Four hours cost 75 + 45 \times 4 = 75 + 180 = \$255. The fee is added once, not once per hour.

Graph of a plumber's cost = 75 + 45h for 0 to 6 hours. The line starts at 75 dollars when h = 0 (the one-time fee) and rises 45 dollars for each hour. The point (4, 255 dollars) is marked: 75 + 45 × 4 = 255.Plumber: cost = 75 + 45h0123456$0$100$200$300$400cost ($)h = hours worked$75 fee (at h = 0)(4, $255)+$45 each hour

Unit price comparisons. To find the better buy, divide each price by its quantity and compare the unit prices. The bigger package is often — but not always — cheaper per unit.

Money answers are rounded to the nearest cent at the end. Rounding early can make you a cent or more off, which may not match the answer choices.

3. Rounding in context and working backwards

Round to whole items — but which way? The situation decides, not the usual "5 or more" rule.

SituationRoundExample
You must buy enough (boxes of tile, cans of paint, buses)up8.2 boxes needed → buy 9
You can only make or fill complete ones (servings, full bags)down6.7 servings → 6 full servings
Moneyto the cent$43.5834 → $43.58
Two number lines. Top: 8.2 boxes needed rounds UP to 9, because you must buy enough. Bottom: 6.7 servings rounds DOWN to 6, because only complete servings count.The situation decides which way to round789108.2 boxes neededbuy 9 (round UP)56786.7 servingsmake 6 full (round DOWN)

Working backwards. When a problem gives the end result and asks for the start, undo each step in reverse order with the opposite operation.

Example: Jo had some money. She spent $15 on lunch, then spent half of what was left on a shirt. She has $20 left. How much did she start with?

Work-backwards diagram. Forwards: start with an unknown amount, subtract 15 dollars to get 40 dollars, then spend half to have 20 dollars left. Backwards (blue arrows): 20 dollars times 2 is 40 dollars, then 40 dollars plus 15 dollars is 55 dollars at the start.Start: ?$40$20 left− $15spend half× 2+ $15Backwards: $20 × 2 = $40, then $40 + $15 = $55 at the start
  • Last step was "spend half" → undo by doubling: 20 \times 2 = 40.
  • First step was "spend $15" → undo by adding: 40 + 15 = 55.
  • She started with $55. Check forwards: 55 - 15 = 40; half of 40 is 20 spent; 40 - 20 = 20 left ✓.

Comparing options. For "which is cheaper" questions, compute the full cost of every option for the same situation, then compare. Don't stop after the first option that "seems" cheap.

Formula

Formulas (on the GED formula sheet)

\text{total cost} = (\text{number of units}) \times (\text{price per unit}) d = rt \qquad (\text{distance} = \text{rate} \times \text{time})

Rearranged versions you will use constantly:

\text{price per unit} = \frac{\text{total cost}}{\text{number of units}} \qquad t = \frac{d}{r} \qquad \text{gallons used} = \frac{\text{miles}}{\text{miles per gallon}}

Fixed fee plus a rate: \text{cost} = \text{fee} + (\text{rate}) \times (\text{amount}).

The total cost formula and distance = rate × time are on the GED formula sheet. The rearranged versions and the fixed-fee model are not printed — you build them from the originals by undoing multiplication with division.

Worked example

Example 1 (easy): a grocery total

Maya buys 3 pounds of apples at $1.29 per pound and 2 gallons of milk at $3.49 per gallon. What is her total?

Bar model drawn to scale: three blue parts of 1.29 dollars for 3 pounds of apples (3.87 dollars) and two red parts of 3.49 dollars for 2 gallons of milk (6.98 dollars). The whole bar is the total, 10.85 dollars.3 × $1.29 + 2 × $3.49 = $3.87 + $6.98 = $10.85$1.29$1.29$1.29$3.49$3.49apples: 3 lb → $3.87milk: 2 gal → $6.98total: $10.85Estimate: 3 × $1.30 + 2 × $3.50 = $10.90 ✓
  1. Apples: 3 \times 1.29 = 3.87.
  2. Milk: 2 \times 3.49 = 6.98.
  3. Total: 3.87 + 6.98 = 10.85.

Answer: $10.85

Check: Estimate 3 \times \$1.30 + 2 \times \$3.50 = \$3.90 + \$7.00 = \$10.90 — very close ✓.

Worked example

Example 2 (word problem): road-trip gas

A car gets 35 miles per gallon. Gas costs $3.80 per gallon. How much will the gas cost for a 245-mile trip?

Flow diagram: 245 miles, divided by 35 miles per gallon, gives 7 gallons; 7 gallons times 3.80 dollars per gallon gives 26.60 dollars. Check backwards: 26.60 dollars ÷ 3.80 dollars = 7 gallons and 7 × 35 = 245 miles.Chain of rates: miles → gallons → dollars245 milestrip7 gallons245 ÷ 35$26.607 × $3.80÷ 35 mi/gal× $3.80/galCheck backwards: $26.60 ÷ $3.80 = 7 gal; 7 × 35 = 245 mi
  1. Gallons needed: 245 \div 35 = 7 gallons.
  2. Cost: 7 \times 3.80 = 26.60.

Answer: $26.60

Check: Work backwards: \$26.60 \div \$3.80 = 7 gallons; 7 \times 35 = 245 miles ✓.

Worked example

Example 3 (word problem): buying whole packages

A family reunion has 75 guests. Each guest will get 2 hot dogs. Buns come in packs of 8 for $2.79 a pack. How much will the buns cost?

A row of 19 packs of 8 buns over a scale from 0 to 160 buns. A red line marks the 150 buns needed. 18 packs (blue) hold 144 buns, 6 short; the 19th pack (green) brings the total to 152, enough. So buy 19 packs: 19 × 2.79 dollars = 53.01 dollars.150 buns needed ÷ 8 per pack = 18.75 → buy 19 packs135791113151704080120160150 needed18 packs = 14419 packs= 15218 packs is 6 buns short, so round UP: 19 × $2.79 = $53.01
  1. Buns needed: 75 \times 2 = 150.
  2. Packs: 150 \div 8 = 18.75. You can't buy part of a pack, and 18 packs (144 buns) is not enough, so round up to 19 packs.
  3. Cost: 19 \times 2.79 = 53.01.

Answer: $53.01

Check: 19 packs hold 19 \times 8 = 152 \ge 150 buns ✓, and 18 packs hold only 144 ✓.

Worked example

Example 4 (work backwards): find the hours

An electrician charges a $85 service fee plus $55 per hour. A customer's bill is $332.50. How many hours did the electrician work?

Bar model drawn to scale for a 332.50 dollars bill: a red part for the 85 dollars fee, then four blue parts of 55 dollars and a half part (27.50 dollars) for the hours. The hourly part is 332.50 dollars − 85 dollars = 247.50 dollars, and 247.50 dollars ÷ 55 dollars = 4.5 hours.$332.50 = $85 fee + hours × $55fee $85$55$55$55$55½bill: $332.50$332.50 − $85 = $247.50$247.50 ÷ $55 = 4.5 hours
  1. Remove the fixed fee: 332.50 - 85 = 247.50 — this is the hourly part.
  2. Divide by the hourly rate: 247.50 \div 55 = 4.5.

Answer: 4.5 hours (4\tfrac{1}{2} hours)

Check: 85 + 55 \times 4.5 = 85 + 247.50 = 332.50 ✓.

Worked example

Example 5 (GED-hard): compare two plans

Gym A charges a $40 joining fee plus $25 per month. Gym B charges $32 per month with no joining fee. Over one year (12 months), which gym is cheaper, and by how much?

Graph of total cost over 0 to 12 months. Gym A (blue) starts at 40 dollars and rises 25 dollars a month to 340 dollars at 12 months. Gym B (red) starts at 0 dollars and rises 32 dollars a month to 384 dollars. At 12 months Gym A is cheaper by 44 dollars. The lines cross near 5.7 months.Gym A: 40 + 25m vs Gym B: 32m024681012$0$100$200$300$400total cost ($)m = monthsA: $340B: $384$44Lines cross near m ≈ 5.7;after that A is cheaper
  1. Gym A: 40 + 25 \times 12 = 40 + 300 = 340.
  2. Gym B: 32 \times 12 = 384.
  3. Compare: 384 - 340 = 44.

Answer: Gym A is cheaper by $44 for the year.

Check: Gym A costs $7 less per month (32 - 25), so over 12 months it saves 7 \times 12 = \$84, but its fee costs $40: 84 - 40 = 44 ✓.

Calculator tip

Using the TI-30XS MultiView

  • Type a whole step at once to avoid copying errors: 3 × 1.29 + 2 × 3.49 enter → 10.85. The calculator does the multiplications before the addition.
  • Use parentheses when a step must happen first: (332.50 - 85) \div 55 must be typed ( 332.5 − 85 ) ÷ 55. Without parentheses you would get 332.50 - 1.545\ldots.
  • Mixed numbers: use 2nd n/d for 6\tfrac{3}{4}, or type 6.75. Press toggle to switch a fraction answer to a decimal.
  • Previous answer: after enter, pressing an operation key (like ×) automatically starts with the last answer, so you can chain steps without retyping.
  • Rounding: the calculator shows many decimals; you decide whether to round up (whole items to buy), down (complete items you can make) or to the cent.

When NOT to use it: don't let the calculator decide the plan — write the steps first. And estimate before you press enter so a typing slip doesn't go unnoticed.

Common mistake

Common mistakes

  • Stopping one step too early. Wrong: the question asks for the change, and you choose the total cost ($21.55). Right: subtract it from the amount paid ($50 − $21.55 = $28.45).
  • Using the wrong quantity. Wrong: adding one shirt and one pair of socks when 3 and 2 were bought. Right: multiply each price by its quantity first.
  • Treating a fixed fee like a rate. Wrong: hours = \$345 \div \$45. Right: subtract the $75 fee first, then divide: (345 - 75) \div 45 = 6.
  • Rounding the wrong way. Wrong: 8.2 boxes → buy 8. Right: you must buy 9 to have enough. Wrong: 6.7 servings → 7 full servings. Right: 6.
  • Reading a mixed number as a decimal. Wrong: 6\tfrac{3}{4} = 6.34. Right: 6\tfrac{3}{4} = 6.75.
  • Comparing totals instead of unit prices. Wrong: "the $5.76 pack of 24 bottles is cheaper than the $7.92 pack of 36 bottles". Right: compare price per bottle, $0.24 vs $0.22, so the bigger pack is the better buy.
Test strategy

GED test strategy

  • Write the plan in words (on your noteboard) before calculating. It keeps multi-step problems organized and makes errors easy to spot.
  • Estimate first. Round every number and get a ballpark answer; eliminate choices that are far off.
  • Expect "partial" answers among the choices. The GED deliberately includes the answer you would get by stopping one step early (the total instead of the change, one day's pay instead of a week's). Re-read the question before you click.
  • Plug the answer back in for work-backwards questions — it is often faster than solving.
  • Watch the units in the question and the answer choices (hours vs. minutes, feet vs. square feet, dollars vs. cents).
  • Use the formula sheet for total cost and d = rt, and don't overthink: most steps are one of the four operations.
  • Pace yourself: multi-step problems can take 2–3 minutes. If you are stuck, flag it and move on.

Check yourself

Multi-step real-world problems

Luis buys 3 shirts that cost $14.50 each and 2 pairs of socks that cost $4.25 per pair. What is the total cost before tax?

Answer choices
Hint

Find the cost of the shirts and the cost of the socks separately, then add.

Check yourself

Multi-step real-world problemsFill in

Keisha earns $15.80 per hour. She works 32 hours each week for 4 weeks. How much does she earn in the 4 weeks, before taxes?

$

Type your answer in the box. Fractions like 3/4 are fine.

Hint

Find the total number of hours first, then multiply by the hourly rate.

Summary

Recap

  • Use the 4-step plan: understand, plan, solve, check. Label every intermediate result with its unit.
  • Translate clue words, but always ask whether you are finding a total or a rate.
  • Total cost = units × price per unit, and d = rt, are on the formula sheet; rearrange them by dividing.
  • Fixed fee + rate: subtract the fee once before dividing by the rate.
  • Round up to buy enough, down for complete items, and money to the cent at the end.
  • Work backwards by undoing each step in reverse order; compare options by computing each one fully.
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