Geoff and Gina bought 20 books altogether. If Geoff gave 6 of his books to Gina, the number of books he had would be 2 fewer than the number of books Gina had. How many books did each of them buy?
If Geoff bought x books then Gina bought 20-x books
After the book exchange:
Geoff has x-6
Gina has 20-x + 6 = 26-x
Gina - Geoff = 2
26-x - (x-6) = 2
solve for x
Well, it seems like Geoff and Gina are really "book"ing it! So, let's solve this mystery of books together.
Let's call the number of books Geoff initially had G, and the number of books Gina initially had B.
According to the problem, we know that G + B = 20, since they bought 20 books altogether.
Now, if Geoff gave 6 of his books to Gina, the new number of books Geoff would have is G - 6, and Gina would have B + 6 books. It's mentioned that Geoff would have 2 fewer books than Gina at this point, so we can write another equation: G - 6 = B + 6 - 2.
Now, let's simplify that equation a bit: G - 6 = B + 4.
Since we have two equations, we can solve for the unknowns. First, we'll solve for G in terms of B using the first equation: G = 20 - B.
Plugging this into the second equation: 20 - B - 6 = B + 4. Let's simplify that: 14 - B = B + 4.
Now, let's bring all the B terms to one side: 14 - 4 = B + B. Simplifying further: 10 = 2B.
Dividing by 2 on both sides, we find that B = 5.
So, Gina bought 5 books. Since the total number of books is 20, Geoff must have bought the remaining 20 - 5 = 15 books.
So, Geoff bought 15 books, and Gina bought 5 books. "Book"-ylicious!
Let's assume that Gina initially had x books.
Since Geoff gave 6 of his books to Gina, Geoff would have x - 6 books remaining.
According to the information given, Geoff would have 2 fewer books than Gina. So we can represent this mathematically as:
x - 6 = (x - 2)
Simplifying the equation, we get:
x - 6 = x - 2
-6 = -2
This is not possible. There seems to be an error in the question. Please double-check and provide accurate information.
Let's solve this algebraically and use the given information to form equations.
Let's say Geoff bought x books and Gina bought y books.
According to the problem, Geoff and Gina bought a total of 20 books, so we have our first equation:
x + y = 20 ...(Equation 1)
We also know that if Geoff gave 6 of his books to Gina, the number of books he had would be 2 fewer than the number of books Gina had. This means that Geoff would then have (y + 6) - 2 books, and Gina would have y books. Simplifying this information, we have our second equation:
(y + 6) - 2 = y ...(Equation 2)
Now we can solve these two equations simultaneously to find the values of x and y.
Let's start by simplifying Equation 2:
y + 4 = y ...(Equation 2 simplified)
Now, subtracting y from both sides, we get:
4 = 0
This is not possible, as the equation is inconsistent and has no solution. It means there is no way to distribute the books between Geoff and Gina that satisfies all the given conditions.
Therefore, there is no specific answer to how many books each of them bought.