Answer:
Harry had $90 and Kayla had $120 at the beginning.
Step-by-step explanation:
Given:
Initial amount of Harry's money = 75% of Kayla's initial amount.
Harry earned $30 and Kayla earned 25% more.
Harry's final amount = 80% of Kayla's final amount.
Let the initial amount of Kayla be 'x'.
As per question:
Initial amount of Harry's money = 75% of Kayla's initial amount.
Initial amount of Harry's money = 75% of ![x](https://tex.z-dn.net/?f=x)
Initial amount of Harry's money = ![0.75x](https://tex.z-dn.net/?f=0.75x)
Now, Harry earned $30 more. So, total amount of Harry is given as:
Final amount of Harry's money = ![0.75x+30](https://tex.z-dn.net/?f=0.75x%2B30)
Kayla also earned 25% more of her money. So, final amount of Kayla's money is given as:
Kayla's final amount = ![x+25\%\ of\ x=x+0.25x=1.25x](https://tex.z-dn.net/?f=x%2B25%5C%25%5C%20of%5C%20x%3Dx%2B0.25x%3D1.25x)
Now, again as per question:
Harry's final amount = 80% of Kayla's final amount.
![0.75x+30=0.80\times 1.25x](https://tex.z-dn.net/?f=0.75x%2B30%3D0.80%5Ctimes%201.25x)
![0.75x+30=1x](https://tex.z-dn.net/?f=0.75x%2B30%3D1x)
![1x-0.75x=30](https://tex.z-dn.net/?f=1x-0.75x%3D30)
![0.25x=30](https://tex.z-dn.net/?f=0.25x%3D30)
![x=\frac{30}{0.25}=\$120](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B30%7D%7B0.25%7D%3D%5C%24120)
Therefore, initial money Kayla had = $120
Initial money Harry had = ![0.75x=0.75\times 120=\$90](https://tex.z-dn.net/?f=0.75x%3D0.75%5Ctimes%20120%3D%5C%2490)
Hence, Harry had $90 and Kayla had $120 at the beginning.