## Ages and Siblings Problems

Suppose we have three siblings Alf, Ben and Colin. Alf is twice as lod as Colin, and three years younger than Ben. The sum of their ages is 53. How old is each sibling?

We can construct the table

Sibling | Age |

Alf | |

Ben | |

Colin |

\[x\]

and use the relations in the question to write the ages of all the siblings in terms of \[x\]

. If the age of Colin is \[x\]

then the age of Alf is \[2x\]

, and the age of Ben is \[2x+3\]

. The table becomesSibling | Age |

Alf | \[2x\] |

Ben | \[2x+3\] |

Colin | \[x\] |

\[2x+2x+3+x=53 \rightarrow x=10\]

.