SOLUTION: The average age of two sisters is three times the age of the younger one . in seven years' time the sum of their ages will be greater than the difference in their ages by 20 years.

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Question 1201541: The average age of two sisters is three times the age of the younger one . in seven years' time the sum of their ages will be greater than the difference in their ages by 20 years. how old are they now? (The answer is 3 and 15)
so ,
Let x=older sister and y=younger sister
x+y=3y
7+(x+y) greater than (x-y)+20
But how can you form Simultaneous equations from this ? How is it worked out ?
Found 3 solutions by josgarithmetic, Glaviolette, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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The average age of two sisters is three times the age of the younger one .
in seven years' time the sum of their ages will be greater than the difference in their ages by 20 years.
how old are they now? (The answer is 3 and 15)

so ,
Let x=older sister and y=younger sister
x+y=3y
7+(x+y) greater than (x-y)+20
But how can you form Simultaneous equations from this ? How is it worked out ?
-------------------------------------------

j, younger
v, older

To follow the description exactly as written,
system%28%28j%2Bv%29%2F2=3j%2C%28j%2B7%29%2B%28v%2B7%29-%28v-j%29=20%29

Simplifying from that system,
system%28j%2Bv=6j%2Cj%2Bv%2B14-v%2Bj=20%29

system%28j%2Bv=6j%2C2j=6%29

system%28v=5j%2Cj=3%29

Answer by Glaviolette(140) About Me  (Show Source):
You can put this solution on YOUR website!
The average would be represented by (x+y)/2. This is equal to 3y. Then, their ages in 7 years would be x + 7 and y + 7. This sum is greater than the difference of their ages by 20 years. You don’t need to use a >. By adding the 20 to the difference, that is showing that the sum would be greater than the difference by 20.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
The average age of two sisters is three times the age of the younger one . in seven years' time the sum of their ages will be greater than the difference in their ages by 20 years. how old are they now? (The answer is 3 and 15)
 so , 
Let x=older sister   and y=younger sister 
x+y=3y
7+(x+y) greater than (x-y)+20 

But how can you form Simultaneous equations from this ? How is it worked out ?

You don't need simultaneous/Systems of equations for every problem, unless asked to form and/or use them.
This is solved by simply using only 1 (ONE) variable. That's ALL that's needed!

Let the younger's age be Y
Since the average of the ages is thrice the younger's age, then the 2 ages' average is, 3Y, thus
making the sum of their ages, 6Y, with the older's age being 5Y. 

I hope you're following up to this point.

Now, in 7 years'time, the sum of their ages will be 6Y + 2(7) = 6Y + 14
                                                 We then get: 6Y + 14 = (5Y - Y) + 20
                                                              6Y + 14 = 4Y + 20
                                                              6Y - 4Y = 20 - 14
                                                                   2Y = 6
                                                  Younger's age or 
As the older is 5 times the younger's age (5Y), the older is: 5(3) = 15 years-old