There were 288 more red than blue cards. After John used 75% of the red cards and...

[ydubrovensky4]

There were 288 more red than blue cards. After John used 75% of the red cards and 1/3 of the blue cards, there were 53 more blue cards than red cards left. How many red cards did John have at first?


I know that I need to use the information that there were 288 more red than blue cards at first and that there were 53 more blue cards than red cards left after John used 75% of the red cards and 1/3 of the blue cards. However, I am not sure how to set up an equation to represent this information.

I am also not sure how to handle the fact that John used different percentages of the red and blue cards.

This is the equation I got so far
0.25(b + 288) + (2/3)b = b + 53

 

[stapel]

There were 288 more red than blue cards. After John used 75% of the red cards and 1/3 of the blue cards, there were 53 more blue cards than red cards left. How many red cards did John have at first?


I know that I need to use the information that there were 288 more red than blue cards at first and that there were 53 more blue cards than red cards left after John used 75% of the red cards and 1/3 of the blue cards. However, I am not sure how to set up an equation to represent this information.

I am also not sure how to handle the fact that John used different percentages of the red and blue cards.

This is the equation I got so far
0.25(b + 288) + (2/3)b = b + 53

I'm sorry, but I don't understand your equation...? It would be helpful if you defined the variable, and then used logic to create (and explain) the expressions and equations that you develop.

The number of red cards is defined in terms of the number of blue cards, so pick a variable that stands for "the number of blue cards at the beginning"; say, use B. Then what is the expression for the number of red cards? (Hint: Add.)

After John used 3/4 of the red cards and 1/3 of the blue cards, then he was left with 1/4 of the red cards and 2/3 of the blue cards. You are given that (the number of blue cards) was (the number of red cards) plus (53). What equation can you create with this?

 

[Steven G]

Let r = # of red cards at the beginning.
Let b = # of blue cards at the start.
There were 288 more red than blue cards===>r-b = 288 or r = b + 288
John used 75% of the red cards==> there are 25% of the red cards left denoted as .25r
John used 1/3 of the blue cards ===> there are 2/3 of the blue cards left which is denoted by (2/3)b
Now there were 53 more blue cards than red cards left===> (2/3)b - .25r = 53
Let's see what you can do from here.

You have 0.25(b + 288) + (2/3)b = b + 53. Now you need to thing what it means! 0.25(b + 288) + (2/3)b is the number of cards that remain after John used 75% of the red cards and 1/3 of the blue cards. Now b+53 is 53 more than the number of blue cards that were initially present. These two statements are not equal!

After John used some: The number of blue cards is 58 more than the number of red cards. Write this as an equation and solve it for b or r. I actually have the equation (in two variables) written above.

 

[ydubrovensky4]

I'm sorry, but I don't understand your equation...? It would be helpful if you defined the variable, and then used logic to create (and explain) the expressions and equations that you develop.

The number of red cards is defined in terms of the number of blue cards, so pick a variable that stands for "the number of blue cards at the beginning"; say, use B. Then what is the expression for the number of red cards? (Hint: Add.)

After John used 3/4 of the red cards and 1/3 of the blue cards, then he was left with 1/4 of the red cards and 2/3 of the blue cards. You are given that (the number of blue cards) was (the number of red cards) plus (53). What equation can you create with this?

2/3 * B = 1/4 * (B + 288) + 53
B = 300

300 + 288 = 588 red cards at first.

 

[Steven G]

Let's see if your answer is correct.
You start with 588 red cards which means that you start with 300 blue cards.
After John used 75% of the red cards and 1/3 of the blue cards
So now there are 25% of the 588 red cards left and 2/3 of the blue cards left. That is there are 147 red cards left and 200 blue cards left.
Blue now - Red now = 200 - 147 = 53 which is the correct answer.
Good job!