Liam had 75% more magnets than John at first. Liam gave away 200% as many magnets as John. John was left with 25% of the magnets he had at first. What fraction of Liam's magnets did he have in the end?
To solve this problem, let's break it down step by step:
Step 1: Determine the number of magnets John had at first.
Let the number of magnets John had initially be represented by 'x'. John was left with 25% of his initial number of magnets, which can be expressed as 0.25x.
Step 2: Calculate the number of magnets Liam had at first.
Liam had 75% more magnets than John at first. This means Liam had 1.75 times the number of magnets John had initially. Therefore, Liam had 1.75x magnets.
Step 3: Determine the number of magnets Liam gave away.
Liam gave away 200% as many magnets as John. This means Liam gave away 2 times the number of magnets John gave away. If John gave away 0.25x magnets, then Liam gave away 2 * 0.25x = 0.5x magnets.
Step 4: Calculate the number of magnets Liam had in the end.
To find the number of magnets Liam had in the end, we subtract the number of magnets he gave away from the number he had initially. Therefore, Liam had 1.75x - 0.5x = 1.25x magnets.
Step 5: Determine the fraction of Liam's magnets in the end.
To find the fraction of Liam's magnets in the end, divide the number of magnets Liam had in the end by the number of magnets he had initially:
Fraction = (1.25x / 1.75x) = 5/7.
Therefore, Liam had 5/7 or approximately 0.714 of his initial magnets remaining in the end.