Question 545961: Achilles was trying to figure out the ages of three commanders Alexander, Bart, and Cicero, in his army. The sum of their ages was 80; Alexander was two years younger than Bart, and the sum of the ages of Alexander and Bart was 20 more than the age of Cicero. What are their ages?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Achilles was trying to figure out the ages of three commanders Alexander, Bart, and Cicero, in his army.
The sum of their ages was 80; Alexander was two years younger than Bart, and the sum of the ages of Alexander and Bart was 20 more than the age of Cicero.
What are their ages?
:
Write an equation for each statement:
:
" The sum of their ages was 80;"
a + b + c = 80
:
" Alexander was two years younger than Bart,"
a = b - 2
a - b = -2
:
"the sum of the ages of Alexander and Bart was 20 more than the age of Cicero."
a + b = c + 20
a + b - c = 20
Subtract this equation from the 1st equation
a + b + c = 80
a + b - c = 20
-----------------subtraction eliminates a and b, find c
2c = 60
c = 30 yrs is C's age
then
a + b + 30 = 80
add to the 2nd equation
a + b = 50
a - b = -2
------------adding eliminates b, find a
2a = 48
a = 24
I'll let you find b
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