SOLUTION: 10 times my age minus 5 times my brothers age is 100. 10 years ago the square of my age plus the square of my brothers age was also 100. How old is my brother now?
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Question 399463: 10 times my age minus 5 times my brothers age is 100. 10 years ago the square of my age plus the square of my brothers age was also 100. How old is my brother now? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! 10 times my age minus 5 times my brothers age is 100.
10a - 5b = 100
-5b = -10a + 100
Simplify, divide by -5
b = 2a - 20
:
10 years ago the square of my age plus the square of my brothers age was also 100.
(a-10)^2 + (b-10)^2 = 100
replace b with (2a-20)
(a-10)^2 + ((2a-20) - 10)^2 = 100
(a-10)^2 + (2a-30)^2 = 100
FOIL
a^2 - 20a + 100 + 4a^2 - 120a + 900 = 100
Combine like terms
a^2 + 4a^2 - 20a - 120a + 100 + 900 = 100
5a^2 - 140a + 900 = 0
simplify, divide by 5
a^2 - 28a + 180 = 0
Factor
(a-18)(a-10) = 0
a = 18
a = 10
Only a = 18 yrs for your age would work here
:
Find b
b = 2a - 20
b = 2(18) - 20
b = 16 yrs is the brother's age
:
:
Check solution in the 2nd equation
(18-10)^2 + (16-10)^2 =
8^2 + 6^2 = 100
