Answer: There are 48 marbles that Leah has.
Step-by-step explanation:
Since we have given that
Difference between the number of marbles Leah has than Dan has = 28
According to question,
[tex]\dfrac{1}{3}[/tex] of Leah's marble = [tex]\dfrac{4}{5}[/tex] of Dan's marble
[tex]\dfrac{1}{3}L=\dfrac{4}{5}D\\\\L=\dfrac{12}{5}D\\\\\dfrac{L}{D}=\dfrac{12}{5}[/tex]
So, using the ratio, we have
Number of marbles Leah has = 12x
Number of marbles Dan has = 5x
So, our equation becomes,
[tex]12x-5x=28\\\\7x=28\\\\x=\dfrac{28}{7}\\\\x=4[/tex]
So, Number of marbles Leah has [tex]12x=12\times4=48[/tex]
Hence, there are 48 marbles that Leah has.
