Unit Rates in Tables Worksheet 6.2: Solve for missing values and calculate unit rates for various scenarios.

Let's solve each problem step by step. The key concept here is unit rate, which means the rate per one unit of the second quantity (e.g., plants per yard, miles per hour, etc.). We'll use proportional reasoning to find missing values and calculate the unit rate.

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1) Hedging plants vs Distance (yards)

| Hedging plants | 18 | ? | 54 |
|----------------|----|---|----|
| Distance (yards)| 6 | 8 | ? |

- Unit rate = Plants per yard = $ \frac{18}{6} = 3 $ plants per yard.
- So, for 8 yards: $ 3 \times 8 = 24 $ plants.
- For 54 plants: $ \frac{54}{3} = 18 $ yards.

✔ Unit rate: 3.00 plants per yard
✔ Missing values: 24 plants, 18 yards

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2) Bricks vs Minutes

| Bricks | 18 | ? | 99 |
|--------|----|---|----|
| Minute | 4 | 10 | ? |

- Unit rate = Bricks per minute = $ \frac{18}{4} = 4.5 $ bricks/min
- For 10 minutes: $ 4.5 \times 10 = 45 $ bricks
- For 99 bricks: $ \frac{99}{4.5} = 22 $ minutes

✔ Unit rate: 4.50 bricks/minute
✔ Missing values: 45 bricks, 22 minutes

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3) Distance cycled (miles) vs Hours

| Distance cycled (miles) | 38 | 57 | ? |
|-------------------------|----|----|---|
| Hours | 4 | ? | 7 |

- Unit rate = Miles per hour = $ \frac{38}{4} = 9.5 $ mph
- For 57 miles: $ \frac{57}{9.5} = 6 $ hours
- For 7 hours: $ 9.5 \times 7 = 66.5 $ miles

✔ Unit rate: 9.50 miles per hour
✔ Missing values: 6 hours, 66.5 miles

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4) Number of Washes vs Boxes of detergent

| Number of Washes | 275 | 440 | ? |
|------------------|-----|-----|---|
| Boxes of detergent | 5 | ? | 14 |

- Unit rate = Washes per box = $ \frac{275}{5} = 55 $ washes/box
- For 440 washes: $ \frac{440}{55} = 8 $ boxes
- For 14 boxes: $ 55 \times 14 = 770 $ washes

✔ Unit rate: 55.00 washes per box
✔ Missing values: 8 boxes, 770 washes

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5) Pots of Paint vs Coverage (sq. ft)

| Pots of Paint | 5 | 9 | ? |
|---------------|---|---|---|
| Coverage (sq. ft) | 3000 | ? | 12000 |

- Unit rate = sq. ft per pot = $ \frac{3000}{5} = 600 $ sq. ft/pot
- For 9 pots: $ 600 \times 9 = 5400 $ sq. ft
- For 12000 sq. ft: $ \frac{12000}{600} = 20 $ pots

✔ Unit rate: 600.00 sq. ft per pot
✔ Missing values: 5400 sq. ft, 20 pots

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6) Pages read vs Hour

| Pages read | 114 | ? | 418 |
|------------|-----|---|-----|
| Hour | 3 | 7 | ? |

- Unit rate = Pages per hour = $ \frac{114}{3} = 38 $ pages/hour
- For 7 hours: $ 38 \times 7 = 266 $ pages
- For 418 pages: $ \frac{418}{38} = 11 $ hours

✔ Unit rate: 38.00 pages/hour
✔ Missing values: 266 pages, 11 hours

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7) Gallons of fuel vs Miles

| Gallons of fuel | 7 | 4 | ? |
|-----------------|---|---|---|
| Miles | ? | 168 | 504 |

- Unit rate = Miles per gallon = $ \frac{168}{4} = 42 $ miles/gallon
- For 7 gallons: $ 42 \times 7 = 294 $ miles
- For 504 miles: $ \frac{504}{42} = 12 $ gallons

✔ Unit rate: 42.00 miles/gallon
✔ Missing values: 294 miles, 12 gallons

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8) Pizzas vs Cost

| Pizzas | 8 | 5 | ? |
|--------|---|---|---|
| Cost | $54 | ? | $135 |

- Unit rate = Cost per pizza = $ \frac{54}{8} = 6.75 $ dollars/pizza
- For 5 pizzas: $ 6.75 \times 5 = 33.75 $
- For $135: $ \frac{135}{6.75} = 20 $ pizzas

✔ Unit rate: $6.75 per pizza
✔ Missing values: $33.75, 20 pizzas

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9) Depth (foot) vs Pressure (bar)

| Depth (foot) | 136 | ? | 782 |
|--------------|-----|---|-----|
| Pressure (bar)| 4 | 7 | ? |

- Unit rate = Feet per bar = $ \frac{136}{4} = 34 $ feet/bar
- For 7 bars: $ 34 \times 7 = 238 $ feet
- For 782 feet: $ \frac{782}{34} = 23 $ bars

✔ Unit rate: 34.00 feet per bar
✔ Missing values: 238 feet, 23 bars

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✔ Final Answers:

| Problem | Unit Rate | Missing Values |
|--------|-----------|----------------|
| 1 | 3.00 plants per yard | 24, 18 |
| 2 | 4.50 bricks/minute | 45, 22 |
| 3 | 9.50 miles/hour | 6, 66.5 |
| 4 | 55.00 washes/box | 8, 770 |
| 5 | 600.00 sq. ft/pot | 5400, 20 |
| 6 | 38.00 pages/hour | 266, 11 |
| 7 | 42.00 miles/gallon | 294, 12 |
| 8 | $6.75 per pizza | $33.75, 20 |
| 9 | 34.00 feet/bar | 238, 23 |

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