Final answer:
To find out how many more marbles Jack had than Jill at the beginning, we can set up an equation based on the given information. By solving the equation, we find that Jack had 84 marbles to start with. Therefore, Jack had 36 more marbles than Jill to start with. Therefore, Jack had 36 more marbles than Jill to start with.
Step-by-step explanation:
To solve this problem, we can set up an equation based on the given information. Let's say Jack had x marbles to start with. According to the problem, Jill has 4/7 as many marbles as Jack, so she would have (4/7)x marbles. When Jack gives Jill 36 marbles, both Jill and Jack have the same number of marbles. This can be represented as:
(4/7)x + 36 = x
Now we can solve this equation to find the value of x, which represents the number of marbles Jack had to start with. We can do this by first multiplying both sides of the equation by 7 to get rid of the fraction:
4x + 252 = 7x
Subtracting 4x from both sides, we get:
252 = 3x
Dividing both sides by 3, we find that:
x = 84
Therefore, Jack had 84 marbles to start with. To find out how many more marbles than Jill Jack had to start with, we can subtract the number of marbles Jill had at the beginning (4/7 * 84) from the number of marbles Jack had:
84 - (4/7 * 84)
Using the equation Jack had 84 marbles, we can substitute this value in:
84 - (4/7 * 84) = 84 - (4 * 12) = 84 - 48 = 36
Therefore, Jack had 36 more marbles than Jill to start with.