Mark is older than Yolanda. The sum of their ages is 35. The difference between their ages is 15. How old is Mark and how old is Yolanda?

Question

 This is a system of equations word problem, and it's super hard, so.. help? >w<

Answer 1

M = Mark's age

Y = Yolanda's age

eq.1.  M + Y = 35

eq. 2.  M - Y = 15

Solve eq. 1 

M+Y = 35

M = 35-Y

Substitute into eq. 2:

35-Y-Y = 15

35 - 2Y = 15

-2Y = - 20

Y = 10 

Yolanda is 10 years old

M + 10 = 35

M = 35 - 10

M = 25

Mark is 25 years old

 

Answer 2

So here's what we know:

m + y = 35 (their age sum is 35)

m - y = 15 (their age difference is 15, and we know that Mark is the elder)

 

From here, we can use the elimination method:

m + y = 35
m - y = 15

----------------

2m = 50

Divide by 2:

m = 25

 

You should be able to find Yolanda's age from here by plugging Mark's back into the original equations.