Leah has 28 more marbles than Dan. 1 3 of Leah’s marbles is equal to 4 5 of Dan’s marbles. Find the number of marbles that Leah has.
To find the number of marbles that Leah has, let's set up an equation.
Let's represent the number of marbles that Dan has as x. Since Leah has 28 more marbles than Dan, the number of marbles Leah has can be represented as x + 28.
Now, we are told that 1/3 of Leah's marbles is equal to 4/5 of Dan's marbles. So, we can set up the equation:
(1/3)(x + 28) = (4/5)(x)
To solve this equation, we can start by simplifying each side. Multiply through by the least common denominator, which is 15:
15 * (1/3)(x + 28) = 15 * (4/5)(x)
5(x + 28) = 12(x)
Next, we can distribute the multiplication:
5x + 140 = 12x
Now, we can get all the x terms on one side of the equation:
12x - 5x = 140
7x = 140
To solve for x, we can divide both sides of the equation by 7:
x = 20
So, Dan has 20 marbles.
Now, we can find the number of marbles that Leah has by substituting x back into the equation:
Leah's marbles = x + 28 = 20 + 28 = 48
Therefore, Leah has 48 marbles.
Dan 's marbles --- x
Leah's marbles ---- x+28
(1/3)(x+28) = (4/5)x
times 15
5(x+28) = 12x
solve for x , then sub into Leah's marbles