SOLUTION: Hi, Here's my fourth and final GRE math prep word problem of the day: If 3 time's Jane's age, in years, is equal to 8 times Beth's age, in years, and the difference between their

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Hi, Here's my fourth and final GRE math prep word problem of the day: If 3 time's Jane's age, in years, is equal to 8 times Beth's age, in years, and the difference between their      Log On


   

Question 170454: Hi,
Here's my fourth and final GRE math prep word problem of the day:
If 3 time's Jane's age, in years, is equal to 8 times Beth's age, in years, and the difference between their ages is 15 years, how old are Jane and Beth?
Thank you,
Julie
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Let J = Jane's age
and B = Beth's age
.
From: "3 time's Jane's age, in years, is equal to 8 times Beth's age"
3J = 8B (equation 1)
.
From: "difference between their ages is 15 years"
J-B = 15 (equation 2)
.
Solving equation 2 for J:
J-B = 15
J = 15+B
.
Plug the above into equation 1 and solve for B:
3J = 8B
3(15+B) = 8B
45+3B = 8B
45 = 5B
9 = B (Beth's Age)
.
Plug the above into equation 2 and solve for J:
J-B = 15
J-9 = 15
J = 24 (Jane's Age)