SOLUTION: 1. If Samantha were three times as old as she was five years ago, she will be sixty less than six times her current age. How old is Samantha? 2. Ryan was born 6 and one-fourth y

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: 1. If Samantha were three times as old as she was five years ago, she will be sixty less than six times her current age. How old is Samantha? 2. Ryan was born 6 and one-fourth y      Log On

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Question 476266: 1. If Samantha were three times as old as she was five years ago, she will be sixty less than six times her current age. How old is Samantha?
2. Ryan was born 6 and one-fourth years after Alexander. The sum of their ages is 66 and eleven-twelfth years. How old is Alexander?
3. Samantha is 8 and two-third years older than Jason. The sum of their ages is 23 years. How old is Jason?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Sam's current age
++a+-+5+ = Sam's age 5 years ago
+3%2A%28a+-+5%29+ = 3 times Sam's age 5 years ago
+6a+-+60+ = 60 less than 6 times her current age
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(1)
+3%2A%28a+-+5%29+=+6a+-+60+
+3a+-+15+=+6a+-+60+
+3a+=+45+
+a+=+15+
Sam is 15
---------
(2)
Let Ryan's age now = +r+
Let Alex's age now = +a+
given:
(1) +r+=+a+-+6.25+
(2) +r+%2B+a+=+66+%2B+11%2F12+
Substitute (1) into (2)
(2) +a+-+6.25+%2B+a+=+66+%2B+11%2F12+
(2) +2a+=+66+%2B+6.25+%2B+.91667+
(2) +2a+=+73.16667+
(2) +a+=+36.583335+
+12%2A.583335+=+7+
Alex is 36 and 7 months
----------------
s = Sam's age now
j = Jason's age now
given:
(1) +s+=+j+%2B+8.666+
(2) +s+%2B+j+=++23+
--------------
By substitution:
(2) +j+%2B+8.666+%2B+j+=+23+
(2) +2j+=+23+-+8.666+
(2) +2j+=+14.333+
(2) +j+=+7.167+
+.167%2A12+=+2+
Jason is 7 years and 2 months old