Completing Two-way Tables Worksheet | Cazoom Maths Worksheets - Free Printable

Problem: Completing Two-Way Tables

#### Section A: Complete the two-way tables

##### Table 1: Types of cupcakes sold by a bakery in one day
We are given the following table and need to fill in the missing values:

| Types of cupcakes | Small | Large | Total |
|-------------------|-------|-------|-------|
| Chocolate | 13 | | |
| Strawberry | | 18 | |
| Total | 21 | | 60 |

Step-by-Step Solution:

1. Total Small Cupcakes:
- The total number of small cupcakes is given as 21.
- We know that 13 of these are chocolate.
- Therefore, the number of strawberry small cupcakes is:
\[
\text{Strawberry (Small)} = \text{Total Small} - \text{Chocolate (Small)} = 21 - 13 = 8
\]

2. Total Large Cupcakes:
- The total number of cupcakes sold is 60.
- The total number of small cupcakes is 21.
- Therefore, the total number of large cupcakes is:
\[
\text{Total Large} = \text{Total Cupcakes} - \text{Total Small} = 60 - 21 = 39
\]

3. Chocolate Large Cupcakes:
- We know the total number of chocolate cupcakes is the sum of small and large chocolate cupcakes.
- Let \( x \) be the number of large chocolate cupcakes.
- The total number of chocolate cupcakes is:
\[
\text{Chocolate (Total)} = \text{Chocolate (Small)} + \text{Chocolate (Large)} = 13 + x
\]
- Since the total number of large cupcakes is 39 and we know 18 of them are strawberry, the remaining must be chocolate:
\[
\text{Chocolate (Large)} = \text{Total Large} - \text{Strawberry (Large)} = 39 - 18 = 21
\]

4. Strawberry Total Cupcakes:
- The total number of strawberry cupcakes is the sum of small and large strawberry cupcakes:
\[
\text{Strawberry (Total)} = \text{Strawberry (Small)} + \text{Strawberry (Large)} = 8 + 18 = 26
\]

5. Chocolate Total Cupcakes:
- The total number of chocolate cupcakes is:
\[
\text{Chocolate (Total)} = \text{Chocolate (Small)} + \text{Chocolate (Large)} = 13 + 21 = 34
\]

Completed Table:

| Types of cupcakes | Small | Large | Total |
|-------------------|-------|-------|-------|
| Chocolate | 13 | 21 | 34 |
| Strawberry | 8 | 18 | 26 |
| Total | 21 | 39 | 60 |

---

##### Table 2: Information about 80 school students
We are given the following table and need to fill in the missing values:

| | Boy | Girl | Total |
|----------------|-------|-------|-------|
| Right-handed | | 21 | 34 |
| Left-handed | 16 | | |
| Total | | | 80 |

Step-by-Step Solution:

1. Right-handed Boys:
- The total number of right-handed students is 34.
- The number of right-handed girls is 21.
- Therefore, the number of right-handed boys is:
\[
\text{Right-handed (Boy)} = \text{Total Right-handed} - \text{Right-handed (Girl)} = 34 - 21 = 13
\]

2. Left-handed Girls:
- The total number of left-handed boys is 16.
- Let \( x \) be the number of left-handed girls.
- The total number of students is 80.
- The total number of right-handed students is 34, so the total number of left-handed students is:
\[
\text{Total Left-handed} = \text{Total Students} - \text{Total Right-handed} = 80 - 34 = 46
\]
- Therefore, the number of left-handed girls is:
\[
\text{Left-handed (Girl)} = \text{Total Left-handed} - \text{Left-handed (Boy)} = 46 - 16 = 30
\]

3. Total Boys:
- The total number of boys is the sum of right-handed and left-handed boys:
\[
\text{Total (Boy)} = \text{Right-handed (Boy)} + \text{Left-handed (Boy)} = 13 + 16 = 29
\]

4. Total Girls:
- The total number of girls is the sum of right-handed and left-handed girls:
\[
\text{Total (Girl)} = \text{Right-handed (Girl)} + \text{Left-handed (Girl)} = 21 + 30 = 51
\]

Completed Table:

| | Boy | Girl | Total |
|----------------|-------|-------|-------|
| Right-handed | 13 | 21 | 34 |
| Left-handed | 16 | 30 | 46 |
| Total | 29 | 51 | 80 |

---

#### Section B: Solve the problems using two-way tables

##### Problem 1: Homework survey
Ishani conducted a survey on 50 students, of which 21 were Year 7 students. The survey results are:
- 16 Year 7 students do less than an hour of homework each weekend.
- 22 Year 11 students do more than an hour of homework each weekend.

We need to complete the two-way table and compare the amounts of homework done by Year 7 and Year 11 students using percentages.

Step-by-Step Solution:

1. Total Year 11 Students:
- The total number of students surveyed is 50.
- The number of Year 7 students is 21.
- Therefore, the number of Year 11 students is:
\[
\text{Year 11 (Total)} = \text{Total Students} - \text{Year 7 (Total)} = 50 - 21 = 29
\]

2. Year 7 Students Doing More Than an Hour:
- The total number of Year 7 students is 21.
- The number of Year 7 students doing less than an hour is 16.
- Therefore, the number of Year 7 students doing more than an hour is:
\[
\text{Year 7 (More than an hour)} = \text{Year 7 (Total)} - \text{Year 7 (Less than an hour)} = 21 - 16 = 5
\]

3. Year 11 Students Doing Less Than an Hour:
- The total number of Year 11 students is 29.
- The number of Year 11 students doing more than an hour is 22.
- Therefore, the number of Year 11 students doing less than an hour is:
\[
\text{Year 11 (Less than an hour)} = \text{Year 11 (Total)} - \text{Year 11 (More than an hour)} = 29 - 22 = 7
\]

4. Total Students Doing Less Than an Hour:
- The total number of students doing less than an hour is the sum of Year 7 and Year 11 students doing less than an hour:
\[
\text{Total (Less than an hour)} = \text{Year 7 (Less than an hour)} + \text{Year 11 (Less than an hour)} = 16 + 7 = 23
\]

5. Total Students Doing More Than an Hour:
- The total number of students doing more than an hour is the sum of Year 7 and Year 11 students doing more than an hour:
\[
\text{Total (More than an hour)} = \text{Year 7 (More than an hour)} + \text{Year 11 (More than an hour)} = 5 + 22 = 27
\]

Completed Table:

| | Year 7 | Year 11 | Total |
|----------------|--------|---------|-------|
| Less than an hour | 16 | 7 | 23 |
| More than an hour | 5 | 22 | 27 |
| Total | 21 | 29 | 50 |

Comparison Using Percentages:

- Year 7 Students:
- Percentage doing less than an hour:
\[
\frac{16}{21} \times 100 \approx 76.19\%
\]
- Percentage doing more than an hour:
\[
\frac{5}{21} \times 100 \approx 23.81\%
\]

- Year 11 Students:
- Percentage doing less than an hour:
\[
\frac{7}{29} \times 100 \approx 24.14\%
\]
- Percentage doing more than an hour:
\[
\frac{22}{29} \times 100 \approx 75.86\%
\]

Conclusion:
- Year 7 students spend more time doing less than an hour of homework (76.19%) compared to Year 11 students (24.14%).
- Year 11 students spend more time doing more than an hour of homework (75.86%) compared to Year 7 students (23.81%).

---

##### Problem 2: Commuters using a train company
We are given the following information:
- 4% of commuters are under 18 and travel during peak-time.
- 71% of all commuters travel during off-peak.
- 37% of all commuters are over 18.

We need to complete the two-way table and find the percentage of commuters who are under 18 and travel during off-peak.

Step-by-Step Solution:

1. Define Variables:
- Let \( P \) be the percentage of commuters traveling during peak-time.
- Let \( O \) be the percentage of commuters traveling during off-peak.
- We know:
\[
O = 71\%
\]
\[
P = 100\% - O = 100\% - 71\% = 29\%
\]

2. Peak-Time Commuters:
- 4% of commuters are under 18 and travel during peak-time.
- Let \( U \) be the percentage of commuters who are under 18.
- Let \( O_18 \) be the percentage of commuters who are over 18.
- We know:
\[
O_18 = 37\%
\]
\[
U = 100\% - O_18 = 100\% - 37\% = 63\%
\]

3. Off-Peak Commuters Under 18:
- The percentage of commuters who are under 18 and travel during peak-time is 4%.
- Therefore, the percentage of commuters who are under 18 and travel during off-peak is:
\[
U_{\text{Off-peak}} = U - U_{\text{Peak}} = 63\% - 4\% = 59\%
\]

4. Complete the Two-Way Table:

| | Peak-Time | Off-Peak | Total |
|----------------|-----------|----------|-------|
| Under 18 | 4% | 59% | 63% |
| Over 18 | | | 37% |
| Total | 29% | 71% | 100% |

5. Over 18 Commuters During Peak-Time:
- The total percentage of commuters during peak-time is 29%.
- The percentage of under 18 commuters during peak-time is 4%.
- Therefore, the percentage of over 18 commuters during peak-time is:
\[
O_{\text{Peak}} = P - U_{\text{Peak}} = 29\% - 4\% = 25\%
\]

6. Over 18 Commuters During Off-Peak:
- The total percentage of over 18 commuters is 37%.
- The percentage of over 18 commuters during peak-time is 25%.
- Therefore, the percentage of over 18 commuters during off-peak is:
\[
O_{\text{Off-peak}} = O_18 - O_{\text{Peak}} = 37\% - 25\% = 12\%
\]

Completed Table:

| | Peak-Time | Off-Peak | Total |
|----------------|-----------|----------|-------|
| Under 18 | 4% | 59% | 63% |
| Over 18 | 25% | 12% | 37% |
| Total | 29% | 71% | 100% |

Percentage of Commuters Under 18 and Traveling During Off-Peak:
\[
\boxed{59\%}
\]

---

Final Answers:

1. Table 1:
\[
\boxed{
\begin{array}{|c|c|c|c|}
\hline
\text{Types of cupcakes} & \text{Small} & \text{Large} & \text{Total} \\
\hline
\text{Chocolate} & 13 & 21 & 34 \\
\hline
\text{Strawberry} & 8 & 18 & 26 \\
\hline
\text{Total} & 21 & 39 & 60 \\
\hline
\end{array}
}
\]

2. Table 2:
\[
\boxed{
\begin{array}{|c|c|c|c|}
\hline
& \text{Boy} & \text{Girl} & \text{Total} \\
\hline
\text{Right-handed} & 13 & 21 & 34 \\
\hline
\text{Left-handed} & 16 & 30 & 46 \\
\hline
\text{Total} & 29 & 51 & 80 \\
\hline
\end{array}
}
\]

3. Problem 1:
\[
\boxed{
\begin{array}{|c|c|c|c|}
\hline
& \text{Year 7} & \text{Year 11} & \text{Total} \\
\hline
\text{Less than an hour} & 16 & 7 & 23 \\
\hline
\text{More than an hour} & 5 & 22 & 27 \\
\hline
\text{Total} & 21 & 29 & 50 \\
\hline
\end{array}
}
\]

4. Problem 2:
\[
\boxed{59\%}
\]