SOLUTION: Hi Yvonne is 4 years younger than Paul. The ratio of Yvonne's age to Paul's age is 2:3. In how many years time will be 4 :5 Yvonne and Paul respectively. Thanks

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Question 1199409: Hi
Yvonne is 4 years younger than Paul. The ratio of Yvonne's age to Paul's age is 2:3. In how many years time will be 4 :5 Yvonne and Paul respectively.
Thanks

Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

Yvonne is 4 years younger than Paul.
Flip this around to say that Paul is 4 years older than Yvonne.

x = Yvonne's current age
x+4 = Paul's current age


The ratio of their current ages is 2:3
We can treat that ratio as a fraction and form the equation below so we can solve for x.

x/(x+4) = 2/3
3x = 2(x+4)
3x = 2x+8
3x-2x = 8
x = 8
Yvonne is currently 8 years old.
Paul is currently x+4 = 8+4 = 12 years old.

Note that 8/12 = 2/3 to fit the ratio 2:3 (of Yvonne's current age to Paul's current age).
It's the same idea as saying the ratio 8:12 reduces to 2:3.

---------------------------------------------------------------

Let y be the number of years that elapse so that their future ages (Yvonne to Paul) form the ratio 4:5.

Fast forwarding that amount into the future yields:
8+y = Yvonne's future age
12+y = Paul's future age

Divide these items and set the result equal to 4/5.
Solve for y.

(8+y)/(12+y) = 4/5
5(8+y) = 4(12+y)
40+5y = 48+4y
5y-4y = 48-40
y = 8

We see that 8 years must elapse.

Yvonne will be 8+y = 8+8 = 16 years old.
Paul will be 12+y = 12+8 = 20 years old.
The ratio 16:20 fully reduces to 4:5 after dividing both parts by the GCF 4.
The answer is confirmed.

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---------------------------------------------------------------

Answer: 8 years
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
Yvonne is 4 years younger than Paul. The ratio of Yvonne's age to Paul's age is 2:3.
In how many years time will be 4 :5 Yvonne and Paul respectively.
~~~~~~~~~~~~~~~~~~ 


So, today Yvonna is 4 years younger than Paul AND the ratio of Yvonne's age to Paul's age is 2:3.


    Having a bit of mental calculation skills, the reader just should guess
    that Ivonna's age is 8 years, while Paul's age is 12 years.


    If you want more Math to cover this obvious conclusion, write
    3x for Paul age and 2x for Ivonna age, and use this equality 3x - 2x = 4
        from the problem.  It will give you x = 4, so 

    Ivonna's age is 2*4 = 8 years; Paul's age is 3*4 = 12 age, as stated.



Next, having the difference of 4 years, when their ages will be in the ratio 4:5 ?


    Again, for a person having a bit of mental skills, the answer is clear:


       +----------------------------------------+
       |   in 8 years, when their ages will be  |
       |     16 and 20 years, respectively.     |
       +----------------------------------------+


    And if you want more Math, let Y be the number of years to wait.


    You then write this proportion for ages after Y years

         = 

    and find from the proportion

        5*(8+Y) = 4*(12+Y)

        40 + 5Y = 48 + 4Y

        5Y - 4Y = 48 - 40

           Y    =    8.


ANSWER.  In 8 years.

Solved (in two ways: mentally and with equations, for your better understanding).



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