Final answer:
Leah has 48 marbles. We set up two equations based on the information given and solved them simultaneously to find the number of marbles Leah has.
Step-by-step explanation:
The student's question about Leah and Dan's marbles is a classic algebra problem. To solve it, let's denote the number of marbles Leah has as L and the number of marbles Dan has as D. The problem gives us two equations based on the information provided:
- L = D + 28 (Leah has 28 more marbles than Dan)
- 1/3 * L = 4/5 * D (1/3 of Leah's marbles is equal to 4/5 of Dan's marbles)
We can solve these two equations to find the value of L. First, multiply both sides of the second equation by 3 and 5 to clear the fractions:
5 * L = 12 * D
Now, substitute the value of L from the first equation:
5 * (D + 28) = 12 * D
Distribute the 5 on the left side:
5D + 140 = 12D
Rearrange the terms to solve for D:
140 = 12D - 5D
140 = 7D
Divide both sides by 7:
D = 20
Now that we have the value of D (Dan's marbles), we can find L:
L = D + 28
L = 20 + 28
L = 48
Therefore, Leah has 48 marbles.