Question

Latoya has a large collection of basketball cards. She gave half to a friend and a 1/4 to her brother. She still has 75 cards left. How many did she start with?

Answer 1

Answer: She had 200 cards to start with

Step-by-step explanation:

Let x = the amount of cards she had initially. This means she had x cards to start with.

She gave half of the cards she had to a friend. This means she gave her friend x/2 cards. She is left with with (x-x/2) = x/2 cards.

She also gave 1/4 of the remaining cards to her brother. This means that she gave (1/4 × x/2) = x/8 cards to her brother.

Remaining number of cards will be x/2 - x/8 = (4x-x)/8 = 3x/8

She still has 75 cards left. This means

3x/8 = 75

Cross multiplying with 8, it becomes

3x = 75×8 = 600

x = 600/3 = 200

She had 200 cards to start with.

Answer 2

Latoya started with 300 cards.

Solution:

Given that Latoya has a large collection of basketball cards

She gave half to a friend.  

She gave $\frac{1}{4}$ to her brother.

Number of card left = 75

Need to calculate number of cards Latoya was having at starting.  Let’s assume number of cards at starting be represented by variable x.  As she gave half to a friend,

So number of cards given to friend $=\frac{1}{2} \times x=\frac{x}{2}$

Number of cards given to brother $=\frac{1}{4} \times x=\frac{x}{4}$

Number of cards left = number of cards at starting - number of cards given to friend - Number of cards given to brother

$\begin{array}{l}{\Rightarrow 75=x-\frac{x}{2}-\frac{x}{4}} \\\\ {\Rightarrow 75=x-\left(\frac{x}{2}+\frac{x}{4}\right)} \\\\ {\Rightarrow 75=x-\left(\frac{2 x+x}{4}\right)} \\\\ {\Rightarrow 75=x-\left(\frac{3 x}{4}\right)} \\\\ {\Rightarrow 75=x-3 x=\frac{x}{4}} \\\\ {\Rightarrow 75 \times 4=x} \\\\ {\Rightarrow 300=x}\end{array}$

Number of cards at starting = x = 300