In six years Jill will be twice as old as Amanda. One year ago Jill was nine times older than Amanda. How old is Jill now?

I tried 6 + 2x = x because in six years Jill will be twice Amanda's age, but this doesn't work.

I need a formula to work out but don't know where to start. I don't want the answer, I want to know how to find the formula to figure it out so I can do other problems.

You will need to have two equations with two unknowns. The first equation will be for the "In six years Jill will be twice as old as Amanda." and the second equation will be for the "One year ago Jill was nine times older than Amanda."

So if you use J for Jill and A for Amanda, both equations will have J and A in them.

Jill is 10 , Amanda is 1

10

To solve this problem, let's start by assigning variables to the ages of Jill and Amanda. We'll use J for Jill's current age and A for Amanda's current age.

According to the problem statement, in six years Jill will be twice as old as Amanda. Let's represent Jill's age in six years as J + 6 and Amanda's age in six years as A + 6. Therefore, we can write the equation:

J + 6 = 2(A + 6)

Next, it says that one year ago Jill was nine times older than Amanda. So, Jill's age one year ago would be J - 1 and Amanda's age one year ago would be A - 1. This leads us to the equation:

J - 1 = 9(A - 1)

Now we have a system of two equations:

J + 6 = 2(A + 6)
J - 1 = 9(A - 1)

To solve this system, we can use the method of substitution or elimination. Let's use substitution in this case.

Rearrange the first equation to solve for J:
J = 2(A + 6) - 6
J = 2A + 12 - 6
J = 2A + 6

Substitute this value of J in the second equation:
2A + 6 - 1 = 9(A - 1)
2A + 5 = 9A - 9

Simplify the expression:
7 = 7A

Solve for A:
A = 1

Now substitute the value of A back into the equation to find J:
J = 2(1) + 6
J = 8

Therefore, Jill is currently 8 years old.

If J is Jill's age now, then

J+6 is her age in 6 years.
But Amanda will also be 6 years older: A+6