SOLUTION: Rover was 5 years older than Yolanda. In 10 years he found that 4 times his age exceede twice Yolanda's age by only 50. How old were Rover and Yolanda in the beginning? I tried to

Algebra.Com
Question 1103354: Rover was 5 years older than Yolanda. In 10 years he found that 4 times his age exceede twice Yolanda's age by only 50. How old were Rover and Yolanda in the beginning? I tried to solve this, but my answers wouldn't solve. Could you help me learn how? Thank you!
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52864)   (Show Source): You can put this solution on YOUR website!
.
In Math terms, the condition says THIS:

R = Y + 5                      (1)     ("Rover was 5 years older than Yolanda.")
4*(R + 10) = 2*(Y+10) + 50.    (2)     ("In 10 years . . .  4 times his age exceeds twice Yolanda's age by only 50.")


Simplify (2):

4R + 40 = 2Y + 20 + 50,

4R = 2Y + 70 - 40

4R = 2Y + 30.                  (3)


Next, substitute (1) into eq(3). You will get

4*(Y+5) = 2Y + 30,   or

4Y + 20 = 2Y + 30,

2Y = 30 - 20 = 10  ====>  Y =  = 5.


Then  from (1)  R = Y + 5 = 5+5 = 10.


Answer.  At the beginning, R was 10 years old;  Y was 5 years old.

Solved.

------------------
There is a bunch of lessons on age word problems
    - Age problems and their solutions
    - A fresh formulation of a traditional age problem
    - Really intricate age word problem
    - Selected age word problems from the archive
    - Age problems for mental solution
in this site.

Read them and become an expert in solving age problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Age word problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



Answer by greenestamps(13206)   (Show Source): You can put this solution on YOUR website!


My thought for setting up this problem was to use the ages after the 10 years to set up the problem. Rover will always be 5 years older the Yolanda, so

let x = Yolanda's age after the 10 years
then x+5 is Rover's age then

The problem says 4 times Rover's age at this time is 50 more than twice Yolanda's age:





Yolanda's age after the 10 years is 15, so her age at the beginning was 5; that means Rover's age at the beginning was 10.
RELATED QUESTIONS

Rover Boy was 5 years older than Yolanda. In 10 years he found that 4 times his age... (answered by stanbon)
Harold was 5 years older than phidella. In 10 years he found that 4 times his age... (answered by ankor@dixie-net.com)
Will is twice Vanessa's age. 14 years ago, he was 4 times older than Vanessa. FInd their... (answered by josgarithmetic)
If the Fathers age is 5 times his son's age. 4 years back the father was 9 times older... (answered by Theo,ikleyn,kiks)
Author is 10 years older than Carol. 9 years ago his age was 3 times her age. How old... (answered by josmiceli)
peter is 4 times older than mark. in 10 years he will only be twice as old as mark. what... (answered by Alan3354)
John is 5 years older than Mary. In 10 years, twice John’s age decreased by Mary’s age is (answered by josgarithmetic)
vincent is 10 years older than john paul. 5 years ago, his age was twice that of john... (answered by mananth)
.A father is twice as old as his son. 20 years ago, the age of the father was 12 times... (answered by josgarithmetic)