SOLUTION: Shelias age is two years more than twice Nicole’s age. The sum of their ages is the same as Steve’s age. If Steve’s age is ten years less than five times Nicole’s age, find the age

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Question 1124069: Shelias age is two years more than twice Nicole’s age. The sum of their ages is the same as Steve’s age. If Steve’s age is ten years less than five times Nicole’s age, find the age of each.
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Shelia’s age now
Let +b+ = Nicole’s age now
Let +c+ = Steve’s age now
———————————————-
(1) +a+=+2b+%2B+2+
(2) +a+%2B+b+=+c+
(3) +c+=+5b+-+10+
————————————
Plug (2) into (3)
(3) +a+%2B+b+=+5b+-+10+
(3) +a+=+4b+-+10+
Plug (3) into (1)
(1) +4b+-+10+=+2b+%2B+2+
(1) +2b+-+5+=+b+%2B+1+
(1) +b+=+6+
And
(1) +a+=+2%2A6+%2B+2+
(1) +a+=+14+
And
(3) +c+=+5%2A6+-+10+
(3) +c+=+20+
———————————
Check:
(2) +14+%2B+6+=+20+
OK
Shelia is 14
Nicole is 6
Steve is 20

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Shelias age is two years more than twice Nicole’s age. The sum of their ages is the same as Steve’s age. If Steve’s age is ten years less than five times Nicole’s age, find the age of each. 
Let Nicole's be N

Then Sheila's = 2N + 2 

Also, Steve's is: N + 2N + 2, or 3N + 2

We then get: 3N + 2 = 5N - 10

3N - 5N = - 10 - 2

- 2N = - 12

N, or Nicole is: 

Sheila is: 2(6) + 2, or 14 years-old

Steve is: 3(6) + 2 = 20 years-old

That's it!! Nothing COMPLEX!!