jackie and janice are sisters with the same birthday, different birth years. today jackie is four times as old as janice. next year she will 3 times as old as janice. if jackie is less than 10 this year how old will she be next year?

To solve this problem, we can start by assigning variables to the ages of Jackie and Janice. Let's say that Jackie's current age is "J" and Janice's current age is "Jn". Also, let's say their birth years are represented by "y" and "yn", respectively.

We are given that Jackie and Janice have the same birthday but were born in different years, which means that the difference in their ages is equal to the difference in their birth years. So, we have the equation: J - Jn = y - yn.

We are also given that currently Jackie is four times as old as Janice. So, we have J = 4 * Jn.

Additionally, we know that next year, Jackie will be three times as old as Janice. So, we can set up the following equation: J + 1 = 3 * (Jn + 1).

Since we know Jackie's current age is less than 10, we can substitute J < 10 into the equations to help us solve.

Substituting equation J = 4 * Jn into J - Jn = y - yn, we get:
4 * Jn - Jn = y - yn.
This simplifies to 3 * Jn = y - yn.

Solving for y - yn, we get:
y - yn = 3 * Jn.

Since Jackie is less than 10 years old, as given in the problem, we can use J < 10 to further simplify the equation:
10 - yn = 3 * Jn.

Now, let's substitute J + 1 = 3 * (Jn + 1) into the equation:
(4 * Jn) + 1 = 3 * (Jn + 1).

Simplifying, we get:
4 * Jn + 1 = 3 * Jn + 3.

Subtracting 3 * Jn from both sides, we get:
Jn + 1 = 3.

Subtracting 1 from both sides, we find:
Jn = 2.

Now, substituting Jn = 2 into the equation 3 * Jn = y - yn, we find:
3 * 2 = y - yn.
6 = y - yn.

Since Jackie is four times as old as Janice, Jackie's current age (J) is equal to 4 times Janice's current age (Jn): J = 4 * 2 = 8.

To find Jackie's age next year, we can substitute J = 8 into J + 1 = 3 * (Jn + 1):
8 + 1 = 3 * (2 + 1).

Simplifying, we get:
9 = 3 * 3.

Therefore, Jackie will be 9 years old next year.