two sisters together have 20 books. if the younger sister lost 3 books and the older sister doubled the number she has, they would have a total of 30 books. How many books does each have?

The older has 26 and the younger 4

Now:

older sister --- x
younger sister --- 20-x

new scenario:
older sister --- 2x
younger --- 20-x - 3 = 17-x

2x + 17-x = 30
x = 13

so now the older has 13, the younger has 7

To solve this problem, we can use algebraic equations. Let's denote the number of books the younger sister has as "x" and the number of books the older sister has as "y."

We are given two pieces of information:

1. The total number of books they have is 20: x + y = 20.

2. If the younger sister loses 3 books (x - 3) and the older sister doubles her number of books (2 * y), the total number of books becomes 30: (x - 3) + 2y = 30.

We can now solve this system of equations to find the values of x and y.

Rearranging the first equation, we get x = 20 - y. Plugging this into the second equation, we have (20 - y - 3) + 2y = 30.

Simplifying the equation, we have: 17 + y = 30 - 2y.

Combining like terms, we get: 3y = 13.

Dividing both sides by 3, we find: y = 13/3.

Since we cannot have fractional values for the number of books, we can conclude that this problem has no integer solution.