231k views
1 vote
Ana has 24 more cards than Diana. 3/5 of Diana’s cards equal 1/2 of Ana’s cards. How many cards does Ana have?

User Szymonm
by
4.1k points

1 Answer

1 vote

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


(3)/(5) of Diana’s cards equal
(1)/(2) of Ana’s cards

Therefore,


(3)/(5) * \text{ number of cards with Diana} = (1)/(2) * \text{ number of cards with Ana}


(3)/(5)y = (1)/(2)x\\\\(3y)/(5) = (x)/(2)\\\\3y * 2 = x * 5\\\\6y = 5x\\\\y = (5x)/(6)

Substitute the above equation of "y" in eqn 1


x = 24 + (5x)/(6)\\\\x = (144 + 5x)/(6)\\\\6x = 144 + 5x\\\\x = 144

Thus number of cards with Ana is 144

User Sandeep Dhull
by
4.4k points