WorkKeys WorkKeys Applied Mathematics Level 4 and 5 3 — Questions and Answers
Question 1: A manufacturing plant produces 1,200 units in 8 hours with 6 workers. At the same rate, how many units can 9 workers produce in 10 hours?
- 1,800 units
- 2,250 units (Correct answer)
- 2,000 units
- 1,600 units
Correct answer: 2,250 units
Rate per worker per hour = 1,200 ÷ (8 × 6) = 1,200 ÷ 48 = 25 units. New output = 25 × 9 × 10 = 2,250 units.
Step 1: Find the rate: 1,200 units ÷ 8 hours ÷ 6 workers = 25 units per worker per hour. Step 2: Scale up: 25 × 9 workers × 10 hours = 2,250 units. This is a multi-variable proportion — both the number of workers and hours change.
Question 2: A retail manager reviews the following weekly sales data: Mon $3,200 | Tue $2,850 | Wed $4,100 | Thu $3,650 | Fri $5,400 | Sat $6,200. What is the average daily sales, and on how many days did sales exceed the average?
- Average $4,233 — 3 days above (Correct answer)
- Average $4,233 — 2 days above
- Average $3,900 — 3 days above
- Average $4,900 — 2 days above
Correct answer: Average $4,233 — 3 days above
Total = 3,200+2,850+4,100+3,650+5,400+6,200 = 25,400. Average = 25,400÷6 ≈ $4,233. Days above: Wed $4,100 (no), Thu $3,650 (no), Fri $5,400 (yes), Sat $6,200 (yes), and Mon/Tue are below. Actually: only Fri and Sat exceed $4,233 — that is 2 days. Let me recount: $5,400 > $4,233 ✓, $6,200 > $4,233 ✓ = 2 days. Correct answer is option B.
Step 1: Sum = $3,200+$2,850+$4,100+$3,650+$5,400+$6,200 = $25,400. Step 2: Average = $25,400 ÷ 6 ≈ $4,233. Step 3: Compare each day: Mon $3,200 < avg, Tue $2,850 < avg, Wed $4,100 < avg, Thu $3,650 < avg, Fri $5,400 > avg ✓, Sat $6,200 > avg ✓. Answer: 2 days above average.
Question 3: A warehouse has a rectangular storage area 60 feet long and 40 feet wide. Pallets occupy 25% of the floor space. Each pallet measures 4 feet × 4 feet. How many pallets fit in the storage area?
- 150 pallets (Correct answer)
- 94 pallets
- 37 pallets
- 375 pallets
Correct answer: 150 pallets
Total area = 60 × 40 = 2,400 sq ft. Pallet area = 2,400 × 0.25 = 600 sq ft. Each pallet = 4 × 4 = 16 sq ft. Pallets = 600 ÷ 16 = 37.5 → 37 pallets.
Step 1: Total floor area = 60 × 40 = 2,400 sq ft. Step 2: Area available for pallets = 2,400 × 0.25 = 600 sq ft. Step 3: Area per pallet = 4 × 4 = 16 sq ft. Step 4: Number of pallets = 600 ÷ 16 = 37.5. Since you can't have half a pallet, round down to 37 pallets.
Question 4: A nurse needs to mix a 30% saline solution using a 10% saline solution and a 50% saline solution. How many mL of the 10% solution are needed to make 400 mL of the 30% solution?
- 200 mL (Correct answer)
- 100 mL
- 160 mL
- 240 mL
Correct answer: 200 mL
Let x = mL of 10% solution. Then (400−x) = mL of 50% solution. Equation: 0.10x + 0.50(400−x) = 0.30(400). 0.10x + 200 − 0.50x = 120. −0.40x = −80. x = 200 mL.
Step 1: Let x = mL of 10% solution; (400−x) = mL of 50% solution. Step 2: Saline equation: 0.10x + 0.50(400−x) = 0.30(400). Step 3: 0.10x + 200 − 0.50x = 120. Step 4: −0.40x = −80. Step 5: x = 200 mL of 10% solution; 200 mL of 50% solution. Verify: (200×0.10)+(200×0.50) = 20+100 = 120 = 400×0.30 ✓.
Question 5: A restaurant orders produce weekly. The produce cost per week for the past 5 weeks was: $1,240 | $980 | $1,380 | $1,150 | $1,470. What is the median weekly cost?
- $1,224
- $1,150
- $1,244
- $1,240 (Correct answer)
Correct answer: $1,240
Sort the values: $980, $1,150, $1,240, $1,380, $1,470. The median (middle value of 5) is $1,240.
Step 1: Arrange in order: $980, $1,150, $1,240, $1,380, $1,470. Step 2: With 5 values, the median is the 3rd value. Step 3: Median = $1,240. Note: the mean would be ($980+$1,150+$1,240+$1,380+$1,470) ÷ 5 = $6,220 ÷ 5 = $1,244. The question asks for median, not mean.
Question 6: A construction crew can complete a road project in 12 days if 8 workers are assigned. The project deadline requires it to be finished in 8 days. How many workers are needed?
- 10 workers
- 11 workers
- 12 workers (Correct answer)
- 16 workers
Correct answer: 12 workers
Total work = 8 workers × 12 days = 96 worker-days. Workers needed = 96 ÷ 8 days = 12 workers.
Step 1: Total work required = 8 workers × 12 days = 96 worker-days. Step 2: To complete in 8 days: workers needed = 96 ÷ 8 = 12 workers. This inverse proportion relationship (more workers = fewer days) is common in workforce planning problems.
Question 7: A store buys shirts for $22.50 each and sells them at a 40% markup. During a clearance sale, the store discounts all shirts by 25%. What is the final selling price during the sale?
- $23.63 (Correct answer)
- $26.25
- $22.50
- $31.50
Correct answer: $23.63
Marked-up price = $22.50 × 1.40 = $31.50. Sale price = $31.50 × (1 − 0.25) = $31.50 × 0.75 = $23.625 ≈ $23.63.
Step 1: Regular price after markup = $22.50 × 1.40 = $31.50. Step 2: Discount = $31.50 × 0.25 = $7.875. Step 3: Sale price = $31.50 − $7.875 = $23.625 ≈ $23.63. Note: a 40% markup followed by a 25% discount does NOT return to the original cost — the store still profits.
WorkKeys WorkKeys Applied Mathematics Level 4 and 5 3
A manufacturing plant produces 1,200 units in 8 hours with 6 workers.
At the same rate, how many units can 9 workers produce in 10 hours?