Leah has 28 more marbles than Dan. 1/3 of Leah's marbles is equal in number to 4/5 of Dan's marbles. Find the number of marbles that Leah has.

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