A **Two-way Table** is used to show totals of a population with two different **properties**, or pieces of information. For example, students in a school can be totalled by year group and by male/female.

Two-way tables can be added vertically to obtain column totals; and horizontally to obtain row totals. The row totals can be added together to obtain a grand total. This should be the same as the column totals added together.

A school is taking a large group of students on an exchange trip. Complete the table, filling in any missing entries, and give the total number of teachers that will be on the trip.

Year 7 | Year 8 | Year 9 | Year 10 | Year 11 | TOTAL | |

Teachers | 1 | 3 | ||||

Girls | 8 | 7 | 6 | 36 | ||

Boys | 3 | 5 | 11 | 27 | ||

TOTAL | 13 | 12 | 12 | 21 | 12 | 70 |

Each time, find a row or column missing one item. Subtract the other numbers in that row or column from the row/column total to find the missing answer.

Year 7 | Year 8 | Year 9 | Year 10 | Year 11 | TOTAL | |

Teachers | 1 | 2 | 1 | 3 | 0 | 7 |

Girls | 8 | 7 | 6 | 7 | 8 | 36 |

Boys | 4 | 3 | 5 | 11 | 4 | 27 |

TOTAL | 13 | 12 | 12 | 21 | 12 | 70 |

Calculations:

Year 7 Boys. Use column total:13 - 8 - 1 = 4

Year 11 Boys. Use Row total: 27 - 4 - 3 - 5 - 11 = 4

Similarly, Year 8, Year 9 teachers and Year 10 girls: use column totals

Year 11 girls, use row totals

Year 11 teachers: use column totals

Add the teachers for a total

Answer: Total number of teachers: 7

A car showroom has 35 cars in total. There are 6 blue cars, 11 are black and the remainder are red. There are three styles: 10 are 3-door cars, 13 are 5-door cars and 12 are SUVs.

Of the 3-door cars, 2 are black and 3 are silver. Of the red cars, 7 are 5-door, Of the SUVs, 3 are silver. How many black SUVs does the car showroom have?

Complete the table given the information in the question.

3-door | 5-door | SUV | TOTAL | |

Black | 2 | 6 | ||

Silver | 3 | 3 | 11 | |

Red | 7 | 18 | ||

TOTAL | 10 | 13 | 12 | 35 |

Then determine the missing values:

3-door | 5-door | SUV | TOTAL | |

Black | 2 | 1 | 3 | 6 |

Silver | 3 | 5 | 3 | 11 |

Red | 5 | 7 | 6 | 18 |

TOTAL | 10 | 13 | 12 | 35 |

Answer: 3

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