Unit Rates in Tables Sheet 6.1 - Practice finding unit rates and filling in missing values in tables.

Let's solve each problem step by step. The goal is to find the unit rate (i.e., the rate per one unit of the independent variable), and then use that to fill in any missing values in the tables.

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1) Miles vs Minutes

| Miles | 6 | 24 | 72 |
|-------|-----|-----|-----|
| Minutes | 5 | 20 | ? |

- Unit rate = miles per minute
→ From first pair: $ \frac{6}{5} = 1.2 $ miles per minute

Now verify with second pair:
$ 1.2 \times 20 = 24 $ ✔

For 72 miles:
$ \text{Minutes} = \frac{72}{1.2} = 60 $

✔ Unit rate: 1.20 miles per minute
Missing value: 60 minutes

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2) Months Subscription vs Cost

| Months | 5 | 9 | ? |
|--------|-----|-----|-----|
| Cost | $35 | $? | $84 |

- Unit rate = cost per month
→ $ \frac{35}{5} = 7 $ dollars per month

So for 9 months: $ 7 \times 9 = 63 $

For $84: $ \frac{84}{7} = 12 $ months

✔ Unit rate: $7.00 per month
Missing values: $63, 12 months

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3) Jugs vs Cups

| Jugs | 2 | ? | 10 |
|------|-----|-----|-----|
| Cups | 9 | 27 | ? |

- Unit rate = cups per jug
→ $ \frac{9}{2} = 4.5 $ cups per jug

For 27 cups: $ \frac{27}{4.5} = 6 $ jugs

For 10 jugs: $ 10 \times 4.5 = 45 $ cups

✔ Unit rate: 4.50 cups per jug
Missing values: 6 jugs, 45 cups

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4) Books vs Boxes

| Books | ? | 96 | 144 |
|-------|-----|-----|-----|
| Boxes | ? | 6 | ? |

We have:
- 96 books in 6 boxes → $ \frac{96}{6} = 16 $ books per box
- So unit rate = 16 books per box

Now:
- For 4 boxes: $ 4 \times 16 = 64 $ books
- For 144 books: $ \frac{144}{16} = 9 $ boxes

✔ Unit rate: 16 books per box
Missing values: 64 books, 9 boxes

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5) Yards vs Seconds

| Yards | ? | 15 | 40 |
|-------|-----|-----|-----|
| Seconds | 4 | 6 | ? |

From second column:
$ \frac{15}{6} = 2.5 $ yards per second

Check with third: $ 2.5 \times ? = 40 $ → $ ? = \frac{40}{2.5} = 16 $ seconds

First column: $ 2.5 \times 4 = 10 $ yards

✔ Unit rate: 2.50 yards per second
Missing values: 10 yards, 16 seconds

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6) Episodes vs Minutes

| Episodes | 3 | ? | 5 |
|----------|-----|-----|-----|
| Minutes | 135 | 360 | ? |

→ $ \frac{135}{3} = 45 $ minutes per episode

So:
- 360 minutes ÷ 45 = 8 episodes
- 5 episodes × 45 = 225 minutes

✔ Unit rate: 45.00 minutes per episode
Missing values: 8 episodes, 225 minutes

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7) Tickets vs Price

| Tickets | 9 | 4 | ? |
|---------|-----|-----|-----|
| Price | ? | $34 | $102 |

→ $ \frac{34}{4} = 8.5 $ dollars per ticket

So:
- 9 tickets: $ 9 \times 8.5 = 76.5 $
- $102 ÷ 8.5 = 12 $ tickets

✔ Unit rate: $8.50 per ticket
Missing values: $76.50, 12 tickets

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8) Railcar vs Length (ft)

| Railcar | 3 | 5 | ? |
|---------|-----|-----|-----|
| Length (ft) | 165 | ? | 440 |

→ $ \frac{165}{3} = 55 $ ft per railcar

So:
- 5 railcars: $ 5 \times 55 = 275 $ ft
- 440 ft ÷ 55 = 8 railcars

✔ Unit rate: 55.00 ft per railcar
Missing values: 275 ft, 8 railcars

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9) Silver Eagles vs Dollars

| Silver eagles | ? | 4 | 12 |
|---------------|-----|-----|-----|
| Dollars | 210 | 140 | ? |

→ $ \frac{140}{4} = 35 $ dollars per eagle

So:
- 210 ÷ 35 = 6 eagles
- 12 × 35 = 420 dollars

✔ Unit rate: $35.00 per eagle
Missing values: 6 eagles, $420

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✔ Final Answers Summary:

| Problem | Unit Rate | Missing Values |
|--------|-----------|----------------|
| 1 | 1.20 miles per minute | 60 minutes |
| 2 | $7.00 per month | $63, 12 months |
| 3 | 4.50 cups per jug | 6 jugs, 45 cups |
| 4 | 16 books per box | 64 books, 9 boxes |
| 5 | 2.50 yards per second | 10 yards, 16 seconds |
| 6 | 45.00 minutes per episode | 8 episodes, 225 minutes |
| 7 | $8.50 per ticket | $76.50, 12 tickets |
| 8 | 55.00 ft per railcar | 275 ft, 8 railcars |
| 9 | $35.00 per eagle | 6 eagles, $420 |

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You can now fill these into the worksheet accordingly! Let me know if you'd like a printable version or visual table.