# Number Problem

## 05 - Sum and Difference of Two Numbers Multiplied to Sum and Difference of Their Squares

**Problem**

Find two numbers such that their sum multiplied by the sum of their squares is 5500, and their difference multiplied by the difference of their squares is 352.

## 04 - In a Mixed Company of ASEAN Nationalities

**Problem**

In a mixed company of Malaysians, Vietnamese, Singaporeans, Thais, and Filipinos, the Malaysians are one less than 1/3 of the Filipinos; and three less than half the Vietnamese. The Filipinos and Thais outnumber the Singaporeans and Vietnamese by 3. The Singaporeans and Filipinos form one less than half the company, and the Singaporeans and Vietnamese form 7/16 of the company. How many persons of each nationality were there?

## 03 - Excess of the Sum of Parts over the Difference of Parts of a Number

**Problem**

The excess of the sum of the half and the third parts over the difference of the fourth and the fifth parts of a number is 188. What is the value of the number?

## 02 - Problems involving sum of two numbers

**Problem 3**

A man bought a cellphone and laptop for P50,000.00, paying three times as much for the laptop as for the cellphone. How much did each cost?

**Problem 4**

Two boys, counting their money, found that together they had P372, and that Rody had ﬁve times as much as Mar. How much had each?

## 01 - Problems involving sum of two numbers

**Problem 1**

The sum of two numbers is 120. If the greater number is four times the less, what are the numbers?

**Problem 2**

The greater of two numbers is twice the less, and the sum of the numbers is 96. What are the numbers?

## Number-related Problems

**Addition**

Expressions that can be translated to addition, ( + ): sum, plus, added to, in addition, increased by, and more than.

Verbal expression | Algebraic equivalent |

the sum of x and y |
x + y or y + x |

x plus y |
x + y |

x increased by y |
x + y |

x added to y |
y + x |

x in addition to y |
y + x |

x more than y |
y + x |

## Verbal Problems in Algebra

The following is an attempt to classify the verbal problems.

**Number-related problems**

Number-related problems are considered as the most basic type of verbal problems. It is taken as the base point of analysis for more complex type of problems.