Mary's sister is 7 years older than Mary. Their combined ages add up to 35. How old is Mary?

Question

I have to solve this problem by writing and solving an equation.  So, M+7=S and M+S=35, what does M equal?

Answer 1

Your initial equations are good.  Two equations with two unknowns can be solved in several different ways.  Two key ways are substitution and elimination:

 

Substitution: (solve one equation for one of the variables, and substitute it into the other)

M+7=S (already solved for S)

M + (M+7) = 35 (plugging "S" into that other equation)

2M + 7 = 35 (combine like terms)

2M = 28 (subtract 7 from both sides)

M = 14 (divide both sides by 2)

From here, you could go on to get S with your first equation by adding 7, so S=21

 

Elimination: (add or subtract equations to each other to eliminate one of the variables)

M-S = -7 (rearrange your first equation)

M+S=35 (second equations)

2M = 28 (add both equations together, and S is eliminated)

M=14 (divide both sides by 2)

 

Note, regardless of method, you should always get the same, correct answers!  This could also be solved by graphing, but that method is typically not as accurate, especially when decimal answers are involved.