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?

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

RELATED QUESTIONS
If you subtract 21 times my age from the square of my age,the result is 100.Find my age (answered by solver91311)

Two years ago my age was three times the square of my son's age. In three years time my... (answered by lwsshak3)

my moms age in years is the same as my brothers age in months. My mothers age is 6... (answered by richwmiller)

If today is my birthday, and my age fifteen years ago is the square of my age fifteen... (answered by ankor@dixie-net.com)

In 10 years from now, my age will be the square of my age 10 years ago. How old am... (answered by josgarithmetic,VFBundy,ikleyn)

My father’s age 5 years ago plus twice my age now gives 65. My age 5 years ago plus... (answered by josgarithmetic,MathTherapy)

tina says my age is four times the difference of my age after four years and my age three (answered by andora)

Miss Scott said 'The sum of my current age and my age 20 years ago is equal to my age in... (answered by josgarithmetic)

my uncle's present age is twice of my sister's age 10 years ago, my uncle's age was... (answered by lwsshak3)