There are 23 black and red cards in a pile. The number of black cards is 4 less than 2 times the number of red cards. How many black cards are in the pile? How many red cards are in the pile?

Question

I don't get how to set it up

Answer 1

Hello Chelsie,

First, we want to assign some expressions for the black and red cards in the pile given the instructions in the problem, okay?

Red Cards = x <-----Not given in the problem.

Black Cards = 2x - 4 <-------"The number of black cards is 4 less than 2 times the number of red."

You are given in the problem, the total number of black and red cards in the pile. That number is 23.

Therefore, the sum of the two expressions we came up with should add up to 23.

x + 2x - 4 = 23 <--------The equation when we add the expressions and set equal to 23.

3x - 4 = 23 <--------Combine like terms.

3x = 27 <---------Add 4 to both sides of our equation.

x = 9 <---------Divide both sides of our equation by 3.

Next, substitute 9 for x for the expression for black cards.

2x - 4

2 (9) - 4 =

18 - 4 = 14

x = 9 <-------Number of red cards.

2x - 4 = 14 <-------Number of black cards

Finally, check our work. We can do this one of two ways. First, we can ask whether the total number of cards equal 23. They do. Another way we can do this is to set up the original equation we used and substituting 9 for x.

x + 2x - 4 = 23

9 + 2(9) - 4 = 23

9 + 18 - 4 = 23

23 = 23

The solution checks out and is valid. I hope I have assisted, and wish you a great weekend. Please feel free to reach out to me for further clarity to the solution, to provide feedback, or request additional assistance by contacting me or any tutor. Best.