if gunnar gives me a cookie, i will have twice as many cookies. if i give gunnar a cookie, we will have the same number of cookies. how many cookies do i have and how many cookies do gunnar have?
He has 3, you have one.
Gunnar has 5 cookies, and you have 7 cookies.
To solve this problem, let's represent the number of cookies you have as "x" and the number of cookies Gunnar has as "y".
According to the first statement, if Gunnar gives you a cookie, you will have twice as many cookies. So, if x is the number of cookies you have, after Gunnar gives you a cookie, you will have x + 1 cookies.
According to the second statement, if you give Gunnar a cookie, you both will have the same number of cookies. So, if y is the number of cookies Gunnar has, after you give him a cookie, you will both have y + 1 cookies.
Now, we can set up two equations based on the given conditions:
1) If Gunnar gives you a cookie, you will have twice as many cookies:
x + 1 = 2y
2) If you give Gunnar a cookie, you will have the same number of cookies:
y + 1 = x
Now we can solve these equations to find the values of x and y.
From equation 2, we can rewrite it as:
x = y + 1
Substituting this value in equation 1, we get:
y + 1 + 1 = 2y
y + 2 = 2y
2 = y
Substituting the value of y back into equation 2, we get:
x = y + 1 = 2 + 1 = 3
Therefore, you have 3 cookies, and Gunnar has 2 cookies.