maggies brother is 13 years younger than twice her age. the sum of their ages is 29. how old is maggie

Question

 this is a elimination or subtraction method I'm pretty sure

 

Answer 1

Let M be Maggie's age and B her brother's age.

Twice Maggie's age is 2M.

13 years younger than that is 2M-13.

B = 2M-13

 

The sum of their ages is 

M + B = 29

 

B =  2M-13

M + B =29

 

We have two equation and two unknowns.  Since one of them is B in terms of M, substitution is easy.

Substitute (2M-13) for B in the second equation and solve for M.

 

M + (2M-13) = 29

3M - 13 = 29

3M = 42

M =14         Answer

 

You could also solve for B.

14 + B = 29

B = 15