The number of cards with Ana is 144
Solution:
Let the number of cards with Ana be "x"
Let the number of cards with Diana be "y"
Given that, Ana has 24 more cards than Diana
number of cards with Ana = 24 + number of cards with Diana
x = 24 + y ----- eqn 1
[tex]\frac{3}{5}[/tex] of Diana’s cards equal [tex]\frac{1}{2}[/tex] of Ana’s cards
Therefore,
[tex]\frac{3}{5} \times \text{ number of cards with Diana} = \frac{1}{2} \times \text{ number of cards with Ana}[/tex]
[tex]\frac{3}{5}y = \frac{1}{2}x\\\\\frac{3y}{5} = \frac{x}{2}\\\\3y \times 2 = x \times 5\\\\6y = 5x\\\\y = \frac{5x}{6}[/tex]
Substitute the above equation of "y" in eqn 1
[tex]x = 24 + \frac{5x}{6}\\\\x = \frac{144 + 5x}{6}\\\\6x = 144 + 5x\\\\x = 144[/tex]
Thus number of cards with Ana is 144
