Respuesta :
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 [tex]x[/tex]
Initial amount of Harry's money = [tex]0.75x[/tex]
Now, Harry earned $30 more. So, total amount of Harry is given as:
Final amount of Harry's money = [tex]0.75x+30[/tex]
Kayla also earned 25% more of her money. So, final amount of Kayla's money is given as:
Kayla's final amount = [tex]x+25\%\ of\ x=x+0.25x=1.25x[/tex]
Now, again as per question:
Harry's final amount = 80% of Kayla's final amount.
[tex]0.75x+30=0.80\times 1.25x[/tex]
[tex]0.75x+30=1x[/tex]
[tex]1x-0.75x=30[/tex]
[tex]0.25x=30[/tex]
[tex]x=\frac{30}{0.25}=\$120[/tex]
Therefore, initial money Kayla had = $120
Initial money Harry had = [tex]0.75x=0.75\times 120=\$90[/tex]
Hence, Harry had $90 and Kayla had $120 at the beginning.
