Question

Latoya had a large collection of basketball cards. she gave half to her friend,Erin. And 1/4 to her brother. She now has 75 cards. How many cards did she start with?

Answer 1

For this case, the first thing we must do is define variables.

We have then:

x: initial amount of cards

We now write the equation that models the problem:

$x - (\frac{1}{2}) x - (\frac{1}{4}) x = 75$

$(\frac{1}{4}) x = 75\\x = 75 * 4\\x = 300$

Therefore, the initial amount of cards is 300

Answer:

Latoya had 300 cards at the beginning

Answer 2

Layota gave away half of her cards and a quarter of her cards, totaling a loss of three-quarters (75%) of her cards. Thus, we know that her remaining cards (75) are 25% of her original total, and thus the total (x) divided by four. We can put this into an equation like the one below, and simply multiply both sides by four to get the original amount of cards Layota started with, 300. 

x/4 = 75 

x = 300