Let x be Billy's age and let y be Danny's age
"Billy is 3 years older than twice Danny's age" can be written as :
x= 3 + 2y ------------------------(1)
" The sum of their ages is 21" can be written as;
x + y = 21 ------------------------(2)
We can now solve equation (1) and (2) simultaneously
Using substitution method;
Substitute equation(1) into equation(2)
U
(3 + 2y) + y = 21
solve for y
3 + 2y + y = 21
3 + 3y = 21
subtract 3 from both-side of the equation
3y = 21 - 3
3y =18
Divide both-side of the equation by 3
y= 6
substitute y = 6 into equation (2) and then solve for x
x + y = 21
x + 6 = 21
subtract 6 from both-side of the equation
x = 21 - 6
x= 15
Hence Billy is 15 years old and Danny is 6 years old