SOLUTION: the sum of two numbers is 7 times their difference. the difference of their squares is twice their sum. find the numbers.

Question 1012475: the sum of two numbers is 7 times their difference. the difference of their squares is twice their sum. find the numbers.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
the sum of two numbers is 7 times their difference.
a + b = 7(a-b)
a + b = 7a - 7b
b + 7b = 7a - a
8b = 6a
simplify, divide by 2
4b = 3a
b = 3a/4
b = .75a
:
the difference of their squares is twice their sum.
a^2 - b^2 = 2(a + b)
a^2 - b^2 = 2a + 2b
substitute for b
a^2 - (.75a)^2 = 2a + 2(.75a)
a^2 - .5625a^2 = 2a + 1.5a
Divide equation by a
a - .5625a = 2 + 1.5
.4375a = 3.5
a = 3.5/.4375
a = 8
Find b
b = .75(8)
b = 6
:
find the numbers. 8 & 6
:
:
:
See if this checks out
8 + 6 = 7(8 - 6)
14 = 7(2)
and
8^2 - 6^2 = 2(8+6)
64 - 36 = 2(14)
RELATED QUESTIONS
i need help in solving this problem: the sum of two numbers is 7 times their difference.... (answered by ankor@dixie-net.com)

find two numbers such that their sum multiplied by the sum of their squares is 5500, and... (answered by oscargut)

The larger of two numbers is twice the smaller. Their sum is three times their... (answered by ankor@dixie-net.com)

the sum of two numbers is 16 and their difference is 5. find the difference of their... (answered by mananth)

The sum of two numbers is 30 and their difference is 6. Find the difference of their... (answered by ikleyn)

The sum of two numbers is 8 and the difference between their squares is 34. Find their... (answered by rakhileshnaidu,Alan3354)

Twice the sum of two numbers is 32. Twice their difference is 4. Find the... (answered by checkley75)

Find two numbers such that their sum multiplied by the sum of their squares is 65, and... (answered by mananth)