4.3 Multi-step workplace problems (3+ steps, payroll+overtime, dilution, volume pricing)
Key Takeaways
- For payroll, split hours at 40 first: regular hours at base pay plus overtime hours at 1.5 times the rate.
- For material cost, compute area or volume, add any waste percentage, then multiply by the unit price.
- For a ratio like 1 to 8, add to 9 total parts, then divide the total quantity by the number of parts.
- For a better-buy decision, reduce every option to price per single unit and choose the lower one.
- Watch for decoy answers equal to a middle step, and confirm the final units before selecting.
Chaining Three or More Steps
The highest-scoring WorkKeys items, at Levels 6 and 7, rarely test a single formula. They ask you to carry a value through three or more operations: compute one quantity, use it to find a second, and combine those to reach the answer. The math on each step is simple. The challenge is organizing the steps and not stopping early. This section walks through the four multi-step patterns you will see most: payroll with overtime, material cost from area or volume, dilution and mixing ratios, and unit-price "better buy" decisions, plus a production-planning example. The test writers know that a tired test-taker often solves the first two steps correctly and then selects that partial result, so many of the wrong answers are exactly the value from a middle step. Slowing down long enough to finish the last operation is usually what separates a Level 5 score from a Level 7 score.
A method for multi-step problems
| Step | Action |
|---|---|
| 1 | Underline exactly what the final answer must be (dollars, gallons, units). |
| 2 | List the given numbers with their units. |
| 3 | Do one operation at a time and write down each result. |
| 4 | Check that the final units match Step 1 before choosing an answer. |
Payroll with regular time plus overtime
Example. A warehouse worker is paid $18.00 per hour for the first 40 hours in a week and time-and-a-half for hours beyond 40. Last week she worked 45 hours. What was her gross pay?
Overtime rate = 18.00 x 1.5 = $27.00 per hour. Regular pay = 40 x 18.00 = $720.00. Overtime hours = 45 - 40 = 5 hours. Overtime pay = 5 x 27.00 = $135.00. Gross pay = 720.00 + 135.00 = $855.00. The trap is multiplying all 45 hours by one rate. Split the hours at 40 first.
Material cost from area, including waste
Example. A floor measures 15 ft by 20 ft. Tile costs $2.40 per square foot, and the installer orders 10 percent extra for cuts and waste. What is the tile cost?
Area = 15 x 20 = 300 sq ft. Add 10 percent waste: 300 x 1.10 = 330 sq ft. Cost = 330 x 2.40 = $792.00. Skipping the waste step gives 300 x 2.40 = $720.00, a common wrong choice placed among the options to catch anyone who stops early.
Dilution and mixing ratios
Ratios describe parts, so first find the total number of parts, then split the total quantity.
Example. A cleaning concentrate is mixed 1 part concentrate to 8 parts water. A crew needs 18 gallons of finished solution. Concentrate costs $24.00 per gallon. What is the concentrate cost for this batch?
Total parts = 1 + 8 = 9 parts. One part = 18 / 9 = 2 gallons. So the batch uses 2 gallons of concentrate and 16 gallons of water (2 x 8 = 16, and 2 + 16 = 18, which checks). Concentrate cost = 2 x 24.00 = $48.00. The frequent error is treating "1 to 8" as 1 out of 8 instead of 1 out of 9 total parts.
The better-buy decision
Compare options by reducing each to a price per single unit, then pick the lower one.
Example. Brand A sells a 32 oz bottle of adhesive for $6.40. Brand B sells a 48 oz bottle for $8.64. Which is the better buy, and by how much per ounce?
Brand A: 6.40 / 32 = $0.20 per oz. Brand B: 8.64 / 48 = $0.18 per oz. Brand B is cheaper at $0.18 per ounce, a saving of 0.20 - 0.18 = $0.02 per ounce. The bigger bottle wins here, but always divide, because the larger size is not automatically cheaper per unit on the real test.
Production planning with a defect rate
Example. A machine produces 250 units per hour and runs for 6.5 hours. About 5 percent of units are defective and discarded. How many good units result?
Total produced = 250 x 6.5 = 1,625 units. Defective = 1,625 x 0.05 = 81.25 units. Good units = 1,625 - 81.25 = 1,543.75, which rounds down to 1,543 good units because you cannot ship a partial unit. An equivalent one-step check is 1,625 x 0.95 = 1,543.75, the same result. If the same line then had to fill orders of 200 good units per pallet, you would divide 1,543 / 200 = 7.7 pallets, meaning only 7 full pallets can ship. That extra division is a fourth step, and it is exactly the kind of chained reasoning the top score levels reward.
Test tips
- Write each intermediate result on your scratch paper so you do not lose a value between steps.
- Watch for decoy answers that equal a correct middle step, such as pay before overtime or area before waste.
- Convert a ratio like "1 to 8" into a total of 9 parts before dividing the quantity.
- For better-buy items, reduce every option to price per one unit and then compare.
- Confirm the final units match the question before selecting, as this single check catches most careless errors.
A technician earns $20.00 per hour for the first 40 hours and time-and-a-half beyond 40. This week he worked 47 hours. What is his gross pay?
A disinfectant is mixed 1 part concentrate to 4 parts water. A crew needs 20 gallons of finished solution. How many gallons of concentrate are required?
Brand X sells a 40 oz container of lubricant for $10.00. Brand Y sells a 60 oz container for $13.20. Which is the better buy per ounce?