# The method of solving problems with percentage

All ratios and formulas for solving problems with percent, are derived from the proportion.

Data of the tasks with percents can be written as the following relations:

All | - | 100% |

Part | - | Part in % |

which can be written as a proportion

All | = | 100% |

Part | Part in % |

Using this proportion, you can get a formulas for the solution of basic types problems with percent.

## Examples of task with percent

Example 1.

Find 15% of 30.
**Solution.**

30 | is | 100% |

x | is | 15% |

write proportion

30 | = | 100% |

x | 15% |

solve the equation

x = | 30 · 15% | = 4.5 |

100% |

**Answer:**15% of 30 is 4.5

Example 2.

35 is what percent of 20?
**Solution.**

20 | is | 100% |

35 | is | x |

write proportion

20 | = | 100% |

35 | x |

solve the equation

x = | 35 · 100% | = 175% |

20 |

**Answer:**35 is 175% of 20.

Example 3.

20 is 5% of what?
**Solution.**

x | is | 100% |

20 | is | 5% |

write proportion

x | = | 100% |

20 | 5% |

solve the equation

x = | 20 · 100% | = 400 |

5% |

**Answer:**20 is 5% of 400.

Percent
Percent Definition. Main information
Decimal to Percent. Percent to Decimal
The method of solving problems with percentage

The most common types of problems with percent:
Find P percent of A
B is P percent of what?
B is what percent of A?
Find the number which is greater (less) than a given number by P percent
Find the number A if known number B which greater (less) than A by P percent

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