Need answer and equation for word problem

Question

beth is 3 times as old as seth, nancy is 6 years older than seth. the sum of their ages is 16. how old is seth?

Answer 1

beth is 3 times as old as seth

 

b = 3s

 

nancy is 6 years older than seth

 

n = s + 6

 

the sum of their ages is 16.

 

b + n + s = 16

 

how old is seth?

 

Solve for s.

 

We have 3 equations:

 

1. b = 3s

2. n = s + 6

3. b + n + s = 16

 

We can use substitution to solve for s.

Use the third equation, but substitute 3s for b:

3s +n + s = 16

4s + n = 16

n = -4s + 16

 

Now, from our second equation, substitute (s + 6) for n:

s + 6 = -4s + 16

5s = 10

s = 2

 

Also from the second equation, if s = 2 then:

n = s + 6

n = 2 + 6

n = 8

 

Now use the first equation, and substitute 2 for s:

b = 3(2)

b = 6

 

Seth is 2, Nancy is 8, and Beth is 6.