Bob had n stickers. Mike has 7 fewer stickers than Bob. then Bob received 9 more stickers from his teacher and Mike lost 6 stickers. They now have 46 stickers in all. how many stickers did Mike have at first?
Let's denote the number of stickers Bob had initially as B.
Since Mike had 7 fewer stickers than Bob, then Mike had B - 7 stickers.
After Bob received 9 additional stickers, he had B + 9 stickers.
After Mike lost 6 stickers, he had B - 7 - 6 = B - 13 stickers.
In total, they had B + B + 9 + B - 13 + 46 = 3B + 42 stickers.
Since they had 46 stickers in total, then 3B + 42 = 46.
Subtracting 42 from both sides, we get 3B = 4.
Dividing both sides by 3, we get B = 4/3 = <<4/3=1.33>>1.33 stickers.
Since B cannot be a fraction, we cannot determine the exact value of B, and thus, we also cannot determine the exact value of Mike's initial number of stickers.
However, if Mike cannot have a fraction of stickers, we can conclude that he had 1 sticker initially. Answer: \boxed{1}.
Let's represent the number of stickers Bob had as "B".
Since Mike has 7 fewer stickers than Bob, we can represent the number of stickers Mike had as "B - 7".
After Bob received 9 more stickers, his total number of stickers became "B + 9".
After Mike lost 6 stickers, his total number of stickers became "(B - 7) - 6".
Together, Bob and Mike have 46 stickers, so we can write the equation:
(B + 9) + ((B - 7) - 6) = 46.
Simplifying the equation:
B + 9 + B - 7 - 6 = 46.
2B - 4 = 46.
2B = 50.
B = 50/2.
B = 25.
Therefore, Bob had 25 stickers at first.
To find the number of stickers Mike had at first, we substitute the value of B into the equation:
B - 7 = 25 - 7 = 18.
Therefore, Mike had 18 stickers at first.
To solve this problem, let's break it down step by step:
Step 1: Let's set up the equations based on the given information.
Let's assume that Bob initially had x stickers.
Mike had 7 fewer stickers than Bob, so he had (x - 7) stickers.
Step 2: After Bob received 9 more stickers from his teacher, his new total is (x + 9).
Mike lost 6 stickers, so his new total is (x - 7 - 6) = (x - 13).
Step 3: The sum of their stickers is 46, so we can write the equation:
(x + 9) + (x - 13) = 46
Step 4: Simplify the equation:
2x - 4 = 46
Step 5: Solve for x:
2x = 50
x = 25
Step 6: Now, we can find the number of stickers Mike had at first.
Mike initially had (x - 7) stickers, so:
Mike had 25 - 7 = 18 stickers.
Therefore, Mike initially had 18 stickers.