SOLUTION: Bill, Phil, and Jenny are siblings. Bill is twice as old as Phil. Jenny is two years younger than Bill. Currently, their dad is twice as old as the sum of their ages. In nine years

Question 979903: Bill, Phil, and Jenny are siblings. Bill is twice as old as Phil. Jenny is two years younger than Bill. Currently, their dad is twice as old as the sum of their ages. In nine years, Dad's new age will be equal to the sum of his three kids' new ages. What is Jenny's current age?
I'm having a lot of trouble understanding this and it's something I need to master before I move on to the next chapter in my math book. Can you help please?
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!

Let b be the Bill's age;
        p be the Phil's age;
        j be the Jenny's age;
and d be the Dad's age.

Then you have 3 equations
b = 2p,
j = b - 2,
d = 2*(b + j + p).

In nine years Bill's age will be (b+9); Jenny's age will be (j+9); Phill's age will be (p+9); and Dad's age will be (d+9).

Thus you have the 4-th equation

d+9 = (b+9) + (j+9) + (p+9).

From the last equation you have

d = b + j + p + 18.

Compare it with the third equation, and you easily get

b + j + p = 18.

So, you have now the system of three equations

.

Substitute b from the first equation into the second and third, and you will eliminate b and reduce the system to the one of two equations in two unknowns:

.

Next, in the obtained system, substitute j from the first equation to the second one. You will get

3p + 2p -2 = 18,   or   5p = 20.

Hence, p = = 4.

And so on . . .

Good luck!

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