SOLUTION: Tom is 5 times as old as Todd. In 5 years Tom's age will be 7 years less than 4 times as old as Todd. How old is Todd?

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: Tom is 5 times as old as Todd. In 5 years Tom's age will be 7 years less than 4 times as old as Todd. How old is Todd?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 575916: Tom is 5 times as old as Todd. In 5 years Tom's age will be 7 years less than 4 times as old as Todd. How old is Todd?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Tom's age now
Let +b+ = Todd's age now
+a+%2B+5+ = Tom's age in 5 yrs
+b+%2B+5+ = Todd's age in 5 yrs
given:
(1) +a+=+5b+
(2) +a+%2B+5+=+4%2A%28+b+%2B+5+%29+-+7+
------------------------
Substitute (1) into (2)
(2) +5b+%2B+5+=+4%2A%28+b+%2B+5+%29+-+7+
(2) +5b+%2B+5+=+4b+%2B+20+-+7+
(2) +b+=+20+-+7+-5+
(2) +b+=+8+
and, since
(1) +a+=+5b+
(1) +a+=+5%2A8+
(10 +a+=+40+
Tom is 40 and Todd is 8
check:
In 5 yrs, Tom will be be 45 and Todd
will be 13 and 4 times Todd's age will be 52
+45+=+52+-+7+
+45+=+45+
OK