Unit Rates in Tables Worksheet 6.1 - Solve for missing values and calculate unit rates in various real-world 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 other quantity (e.g., miles per minute, dollars per ticket, etc.). We'll use proportional reasoning to find missing values and calculate the unit rate.

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1) Miles and Minutes

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

Step 1: Find the unit rate (miles per minute).
From first pair:
6 miles / 5 minutes = 1.2 miles per minute

Check with second pair:
24 miles / 20 minutes = 1.2 → ✔️

Now, for 72 miles:
Time = 72 ÷ 1.2 = 60 minutes

✔ Unit rate = 1.20 miles per minute
✔ Missing time = 60 minutes

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2) Months Subscription and Cost

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

Step 1: Unit rate = cost per month
$35 / 5 months = $7 per month

Now, for 9 months:
Cost = 9 × $7 = $63

For $84:
Months = $84 ÷ $7 = 12 months

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

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3) Jugs and Cups

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

Wait — let’s check consistency:

2 jugs → 9 cups → 9/2 = 4.5 cups per jug

Check next: 9 jugs → 27 cups → 27/9 = 3 cups per jug ✘ Not consistent!

Wait — that can’t be. Let's double-check.

But 2 jugs → 9 cups → 9 ÷ 2 = 4.5 cups per jug
But 9 jugs → 27 cups → 27 ÷ 9 = 3 cups per jug → Inconsistent!

But the problem says "each of the rates remains constant." So there must be a typo or misreading.

Wait — look again:

The table is:
- Jugs: 2 → Cups: 9
- Jugs: ? → Cups: 27
- Jugs: 10 → Cups: ?

Wait — maybe the second row is not 9 jugs? No, it says:
| Jugs | 2 | 9 | 10 |
|------|---|---|----|
| Cups | 9 | 27 | ? |

So:
- 2 jugs → 9 cups → 9 ÷ 2 = 4.5 cups per jug
- 9 jugs → 27 cups → 27 ÷ 9 = 3 cups per jug → Not same

That's impossible if rate is constant.

Wait — perhaps the second column is missing the number of jugs?

No, it says:
Jugs: 2, ?, 10
Cups: 9, 27, ?

So likely:
First: 2 jugs → 9 cups
Second: ? jugs → 27 cups
Third: 10 jugs → ? cups

So we need to find how many jugs give 27 cups, given that 2 jugs → 9 cups.

So ratio: 9 cups / 2 jugs = 4.5 cups per jug

So for 27 cups:
Number of jugs = 27 ÷ 4.5 = 6 jugs

Then for 10 jugs:
Cups = 10 × 4.5 = 45 cups

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

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4) Books and Boxes

| Books | ? | 96 | 144 |
|-------|---|----|-----|
| Boxes | 4 | 6 | ? |

We know:
- 6 boxes → 96 books → 96 ÷ 6 = 16 books per box

So unit rate = 16 books per box

Now:
- For 4 boxes: 4 × 16 = 64 books
- For 144 books: 144 ÷ 16 = 9 boxes

✔ Unit rate = 16.00 books per box
✔ Missing values: 64, 9

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5) Yards and Seconds

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

Given:
- 6 seconds → 15 yards → 15 ÷ 6 = 2.5 yards per second

So unit rate = 2.50 yards per second

Now:
- For 4 seconds: 4 × 2.5 = 10 yards
- For 40 yards: 40 ÷ 2.5 = 16 seconds

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

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6) Episodes and Minutes

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

Given:
- 3 episodes → 135 minutes → 135 ÷ 3 = 45 minutes per episode

So unit rate = 45.00 minutes per episode

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

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

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7) Tickets and Price

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

Given:
- 4 tickets → $34 → $34 ÷ 4 = $8.50 per ticket

So unit rate = $8.50 per ticket

Now:
- For 9 tickets: 9 × 8.50 = $76.50
- For $102: 102 ÷ 8.50 = 12 tickets

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

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8) Railcar and Length

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

Given:
- 3 railcars → 165 ft → 165 ÷ 3 = 55 ft per railcar

So unit rate = 55.00 ft per railcar

Now:
- For 5 railcars: 5 × 55 = 275 ft
- For 440 ft: 440 ÷ 55 = 8 railcars

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

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9) Silver Eagles and Dollars

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

Given:
- 4 eagles → $140 → $140 ÷ 4 = $35 per eagle

So unit rate = $35.00 per eagle

Now:
- For $210: 210 ÷ 35 = 6 eagles
- For 12 eagles: 12 × 35 = $420

✔ Unit rate = $35.00 per eagle
✔ Missing values: 6, $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) | 16.00 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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✔ Complete Table Fill-ins:

1)
Miles: 6, 24, 72
Minutes: 5, 20, 60
Unit rate: 1.20

2)
Months: 5, 9, 12
Cost: $35, $63, $84
Unit rate: $7.00

3)
Jugs: 2, 6, 10
Cups: 9, 27, 45
Unit rate: 4.50

4)
Books: 64, 96, 144
Boxes: 4, 6, 9
Unit rate: 16.00

5)
Yards: 10, 15, 40
Seconds: 4, 6, 16
Unit rate: 2.50

6)
Episodes: 3, 8, 5
Minutes: 135, 360, 225
Unit rate: 45.00

7)
Tickets: 9, 4, 12
Price: $76.50, $34, $102
Unit rate: $8.50

8)
Railcar: 3, 5, 8
Length: 165, 275, 440
Unit rate: 55.00

9)
Silver eagles: 6, 4, 12
Dollars: 210, 140, $420
Unit rate: $35.00

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