Anne has 24 more cards than Devi. Anne finds that 3/5 of Devi's cards are equal to 1/2 of her cards. How many cards does Anne have?
My answer is Anne have 144 cards..
Explanation:
Let x be the num of cards Devi have
x+24 be the num of cards Anne have
* since 3/5 of devis cards is equal to 1/2 of annes cards
So,
3/5x equals to 1/2( x+24)
(*my phone dont have an equal sign so let me use : as an equal sign)
3/5x : 1/2(x+24)
3/5x (2) : x+24
6/5x : x+24
6/5x - x : 24
6x-5x/5 : 24
x/5 : 24
x : 120
Check:
3/5(120) : 1/2(120+24)
72 : 1/2(144)
72 : 72
Let's assume Devi has x number of cards.
According to the statement, Anne has 24 more cards than Devi, so Anne has x + 24 cards.
We are also given that 3/5 of Devi's cards are equal to 1/2 of Anne's cards.
So we can set up the equation:
(3/5) * x = (1/2) * (x + 24)
Now let's solve for x.
Multiplying both sides of the equation by 5/3 to eliminate the fractions, we get:
5/3 * (3/5) * x = 5/3 * (1/2) * (x + 24)
x = 5/3 * 1/2 * (x + 24)
x = 5/6 * (x + 24)
Now let's solve for x.
Multiplying both sides of the equation by 6 to eliminate the fraction, we get:
6 * x = 5 * (x + 24)
6x = 5x + 120
Subtracting 5x from both sides of the equation, we get:
x = 120
So Devi has 120 cards.
Now let's find out how many cards Anne has.
Anne has x + 24 cards.
Substituting the value of x, we get:
Anne has 120 + 24 = 144 cards.
Therefore, Anne has 144 cards.
To find the number of cards Anne has, we first need to determine the number of cards Devi has.
Let's assume Devi has x cards.
According to the given information, 3/5 of Devi's cards are equal to 1/2 of Anne's cards. Mathematically, we can represent this as:
(3/5) * x = (1/2) * (x + 24)
To solve this equation, we can cross-multiply:
3 * (x + 24) = 5 * (1/2) * x
3x + 72 = (5/2) * x
Next, we can bring all the terms involving x to one side of the equation:
(5/2) * x - 3x = -72
(5 - 6/2) * x = -72
(5/2) * x = -72
Now, let's solve for x by multiplying both sides by 2/5:
x = -72 * (2/5)
x = -28.8
Since the number of cards cannot be negative or fractional, we can neglect the negative value and approximate x to the nearest whole number:
x ≈ 29
Therefore, Devi has approximately 29 cards.
Now that we know the number of cards Devi has, we can find the number of cards Anne has by adding 24 to this:
Anne's cards = Devi's cards + 24
Anne's cards = 29 + 24
Anne's cards = 53
So, Anne has approximately 53 cards.