A and B had some paper clips. A gave 40% of his clips to B. B's collection of paper clips rose by 305 to 260. How many paper clips does A had at first.
"B's collection of paper clips rose by 305 to 260"
How can it rise by 305 to reach 260, unless there was a negative number of clips to start with ?
bogus question.
To solve this problem, we can work backwards. Let's first find out how many paper clips B had originally before A gave him 40% of his clips.
We know that B's collection of paper clips increased by 305 to reach a total of 260. Therefore, we can subtract 305 from 260 to find out how many paper clips B had before:
260 - 305 = -45
This result tells us that B had -45 paper clips before A gave him any. That doesn't make sense; we can't have negative paper clips.
The only explanation for this inconsistency is that our assumption is incorrect. We assumed that B started with fewer paper clips than what he actually ended up having. Therefore, B's original paper clip count has to be higher.
Let's assume that B had x paper clips originally. Since A gave B 40% of his clips, that means B's new total of paper clips is 1.4 times his original count (100% + 40% = 140%):
1.4x = 260
Now, we can solve this equation to find x, the original number of paper clips B had:
x = 260 / 1.4
x ≈ 185.71
Since we're dealing with whole numbers, let's round this value down to the nearest whole number:
x = 185
So, B had 185 paper clips originally.
Next, we can calculate how many paper clips A had at the beginning. Since A gave B 40% of his clips, that means A had 60% of the original count:
60% of A's original count = 185
To find A's original count, we need to divide 185 by 0.6:
A's original count = 185 / 0.6
A's original count ≈ 308.33
Rounding down to the nearest whole number for whole paper clips:
A's original count = 308
Therefore, A had 308 paper clips originally.