SOLUTION: John's age is 2 years, less than three times Paul his son,s age. His son Mark is 15 years older than Paul. The sum of their ages is 103. Find the ages of John and histwo sons.

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Question 227094: John's age is 2 years, less than three times Paul his son,s age. His son Mark is
15 years older than Paul. The sum of their ages is 103. Find the ages of John and histwo sons.
Found 2 solutions by josmiceli, drj:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let j= John's age now
Let m= Mark's age now
Let p= Paul's age now
given:
(1) j+=+3p+-+2
(2) m+=+p+%2B+15
(3) j+%2B+p+%2B+m+=+103
Substitute (1) and (2) into (3)
(3) j+%2B+p+%2B+m+=+103
3p+-+2+%2B+p+%2B+p+%2B+15+=+103
5p+%2B+13+=+103
5p+=+90
p+=+18
and, from (1)
(1) j+=+3p+-+2
j+=+3%2A18+-+2
j+=+54+-+2
j+=+52
and, from (2)
(2) m+=+p+%2B+15
m+=+18+%2B+15
m+=+33
John is 52, Paul is 18, Mark is 33
check:
(3) j+%2B+p+%2B+m+=+103
52+%2B+18+%2B+33+=+103
103+=+103
OK

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
John's age is 2 years less than three times Paul his son's age. His son Mark is
15 years older than Paul. The sum of their ages is 103. Find the ages of John and his two sons.

Step 1. Let x be the age of Paul.

Step 2. Let x+15 be the age of Mark since Mark is 15 years older than Paul.

Step 3. Let 3x-2 be the age of John since John is 2 years les than 3 times Paul his son's age.

Step 4. Then, x%2Bx%2B15%2B3x-2=103 or 5x%2B13=103 since the sum of their sages is 103.

Step 5. Solving yields the following steps for the equation 5x%2B13=103

Subtract 13 from both sides of the equation

5x%2B13-13=103-13

5x=90

Divide by 5 to both sides of the equation

5x=90

5x%2F5=90%2F5

x=18, Then 3x-2=52 and x%2B15=33

Check sum of ages: 18%2B52%2B33=103 which is a true statement.

Step 6. ANSWER: John is 52 years old, Mark is 33 years old, and Paul is 18 years old.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV