en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Word Problems >

the sum of two positive numbers is 7 times their difference. the difference of the squares of these numbers is twice the sum of the numbers. find these numbers

Solution

t h e s u m o f tw o p os i t i v e n u mb ers i s 7 t im es t h e i r d i ff ere n ce . t h e d i ff ere n ce o f t h e s q u a res o f t h ese n u mb ers i s tw i ce t h e s u m o f t h e n u mb ers . f in d t h ese n u mb ers

Solution

The numbers : 8, 6

Solution steps

Represent the numbers with

x and y

:

number 1 : x

number 2 : y

A.T.Q.:

x + y = 7 (x - y)

x^{2} - y^{2} = 2 (x + y)

Solve the system of equations:

x + y = 7 (x - y), x^{2} - y^{2} = 2 (x + y) : (x = 8, x = 0, y = 6 y = 0)

Select positive solutions:

6, 8

The numbers : 8, 6

Popular Examples

Dianne is 23 years older than her daughter Amy. In 6 years, Dianne will be twice as old as AMy. How old is amy?The difference of twice a number and 3 is greater than 21 90 is 150% of what number The sum of the smallest and largest of 3 consecutive even integers is 8 less than thrice the middle integer.Determine the integers.a fair die is tossed five times what is th probability of obtaining an even number three times