# In ten years time Mike will be twice as old as his son Ben. 10 years ago mike was 7 times as old as Ben. How old are Mike and Ben now?

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*Hey I am just solving this ques. step by step but not explaining it...*

*lets Mike's age be x years **and Ben's age be y years.*

*According to ques:*

*10years ago,*

*x-10 = 7(y-10)*

*x-10 = 7y-70*

*x-7y+60=0 ----- (1)*

*10years later,*

*x+10 = 2(y+10)*

*x+10 = 2y+20*

*x-2y-10=0 ------ (2)*

*from (1) x = -60+7y ------ (3)*

*putting this value of 'x' in (2),*

*-60+7y-2y-10=0*

*-70+5y=0*

*5y = 70*

*y = 14*

*now from (3),*

*x = -60+7y*

*x = -60+7(14)*

*x = 38*

*thus, age of mike = x years = 38yrs.*

*age of ben = y years = 14yrs.*

Let:

Age of Mike = x, and age of Ben = y

After 10 years age of Mike = x + 10 and

Age of Ben = y + 10

As per data given in the question

x + 10 = 2*(y + 10)

Therefore:

x - 2y = 10 ... ... (1)

Similarly

0 years ago, age of Mike = x - 10 and

Age of Ben = y - 10

As per data given in the question

x - 10 = 2*(y - 10)

Therefore:

x - 7y = -60 ... ... (2)

Subtracting equation (1) from equation (2) we get:

x - 7y - (x - 2y) = -60 -10

Therefore: -5y = -70

Therefore: y = 14

Substituting this value of y in equation (1) we get:

x - 2*14 = 10

Therefore: x = 38

Answer:

Age of Mike is 38 years and that of Bill is 14 years.

Choose Ben's age as x. Then Mike's age is 2x.Ten tears ago, their ages: Mike's = 2x-10 years, and Ben's = x-10 years. Further information tells,

Mike's age 10 years ago = 7*Ben's age (10 years ago), or

2x-10= 7(x-10). We now do some basic operations to see that the unknown x goes to one side and the knowns or numbers go to the otherside as below in the equation:

2x-10 =7(x-10) = 7x-70 or

2x-10 +70 = 7x-70+70,

2x +60=7x

2x+60-2x=7x-2x

60=5x

60/5 =x

x=12 years is the age of Ben.

Mike's age =2x=2*12 = 24 years

Okay here you need to use two variables, one for Mike and one for Ben. So X is Mike and Y is Ben. When you use two variables you have to have at least two equations, and two is enough here. What do we know? First equation is the first sentence. 2X= Y + 10, or in ten years Ben will reach twice Mike's age. Now you could set up a second equation, and solve for Y but why bother? What Y would work if Ben has to be >0 to be alive? And somewhere in her Mike has to be 7 times that old. Start with one, well that gives you Mike as 7, people at 7 don't have children. Try two, okay that would make Mike 14 or 12 at birth, a little young, but, that works with the first equation. Hum, another way to check, and see how old they are. When do we have Mike at twice the age of Ben, so we add in the second factor of '10 years from now'. what numbers happen if we look at the 2, well 2+10 is 12 and the double of that is 24. So, Mike is 24, and Ben is twelve. You can check out other ages for Ben and none of them work. This is what you do if you have forgotten how to do the algebra properly. As I have.