SOLUTION: Four times Mark's present age is 4 more than eight times what Matt's age was two years ago. Three times Matt's present age is 3 more than twice what Mark's age was 4 years ago. F

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: Four times Mark's present age is 4 more than eight times what Matt's age was two years ago. Three times Matt's present age is 3 more than twice what Mark's age was 4 years ago. F      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 335208: Four times Mark's present age is 4 more than eight times what Matt's age was two years ago. Three times Matt's present age is 3 more than twice what Mark's age was 4 years ago. Find their present ages.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
let k = Mark's present age
let t = Matt's present age
:
Write an equation for each statement and simplify:
:
"Four times Mark's present age is 4 more than eight times what Matt's age was two years ago."
4k = 8(t-2) + 4
4k = 8t - 16 + 4
4k = 8t - 12
simplify, divide by 4
k = 2t - 3
;
"Three times Matt's present age is 3 more than twice what Mark's age was 4 years ago."
3t = 2(k-4) + 3
3t = 2k - 8 + 3
3t = 2k - 5
:
Find their present ages.
replace k with (2t-3) in the above equation
3t = 2(2t-3) - 5
3t = 4t - 6 - 5
3t - 4t = -11
-t = -11
t = 11 yrs is Matt's present age
Find k
k = 2t - 3
k = 2(11) - 3
k = 19 yrs is Mark's present age
:
:
Confirm these solution in the statement:
"Four times Mark's present age is 4 more than eight times what Matt's age was two years ago."
4(19) = 8(11-2) + 4
76 = 8(9) + 4