A bag contains white marbles and red marbles, 32 in total. The number of white marbles is 7 less than 2 times the number of red marbles. How many white marbles are there?

Answer 1

We must first place a variable to represent the white and red marbles since there is no number associated with them just yet..

So I would use "x = white marbles" and "y = red marbles."

What we know:

1. There are 32 total marbles so we will use the variables to represent the marbles and create the equation x + y = 32. Where x represents white marbles and y represents red marbles.
2. We also know that the number of white marbles is 7 less than 2 times the number of red marbles. This is where most people get confused. We must set up the equation to represent the white marbles as followed: x = 2y - 7.

What does the question ask:

The question is asking us to find out how many white marbles are there. We know from above that "x = white marbles" and "y = red marbles." We also have two equations as followed: x + y = 32 , and x = 2y - 7. Here we have a system of equations that we can now solve to figure out how many white marbles we have. We can solve this system of equations by a simple substitution. Here are the steps:

1. Since we know x = 2y - 7, we can plug the equation we have for x in the other equation x + y = 32.
2. x + y = 32 , where x = 2y - 7
3. (2y - 7) + y = 32, combine like terms
4. 3y - 7 = 32, move like terms to the same side
5. 3y = 39, solve for y
6. y = 13, which is the number of red marbles.
7. Since we know y = 13, we can now place y in the equation we have for x which is x = 2y - 7.
8. x = 2y - 7, replace y with 13
9. x = 2(13) - 7, solve for x
10. x = 19, which is the number of white marbles

Since "x = white marbles" and "y = red marbles, We have 19 white marbles. If you have any further questions let me know.

Answer 2

This is a systems equation where: W= white marbles; R=red marbles

Therefore:

W + R = 32

W = 2R - 7

For this system, we can use substitution (using an equation to replace a variable in a system of equations)

Since, W = 2R - 7, replace the W in the equation W + R = 32 making it:

(2R - 7) + R = 32

Then solve for R

2R + R - 7 = 32

3R - 7 = 32

+ 7 +7

3R = 39

÷ 3 ÷ 3

R= 13

Now that we solved for R, we can plug this new value into either of the two equations to solve for W. For this problem we'll be re-using the equation W + R = 32 to make things easy.

W + R = 32

W + (13 ) = 32

W + 13 = 32

-13 - 13

W = 19

So in conclusion, there are a total of 19 white marbles out of the 32 total in the bag.

Answer 3

W+R=32

W=2R-7

W=32-R = 2R-7

32-R = 2R-7

3R =39

R=39/3 = 13

R+W=32

13+W = 32

W = 32-13 =19

13 red and 19 white

W=2(13)-7 =26-7=19