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?
:
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