Answer: 48 marbles.
Step-by-step explanation:
Let Leah's marble be represented by y
Let Dan's marble be represented by z.
Leah has 28 more marbles than Dan. This will be written as:
y = z + 28 ....... equation i
1/3 of Leah’s marbles is equal in number to 4/5 of Dan’s marbles. This will be written as:
(1/3 × y) = (4/5 × z)
y/3 = 4z/5
Cross multiply
(5×y) = (3×4z)
5y = 12z ........ equation ii
From equation i, recall that y = z+28. This will be plug into equation ii
5y = 12z
5(z + 28) = 12z
5z+ 140 = 12z
12z - 5z= 140
7z= 140
z = 140/7
z = 20
Dan marble is 20.
Therefore Leah's marble will be:
y= z + 28
= 20+28
= 48
Leah has 48 marbles
