A bag contains white marbles and red marbles, 20 in total. The number of white marbles is 4 less than 2 times the number of red marbles. How many white marbles are there?

Question

Please help me solve this problem I have no idea on what I am suppose to be doing here.

Answer 1

Hi! In order to answer this question you need to set up an algebraic equation.

Lets start with identifying some variables and let

R = # of red marbles

W = # of white marbles

We know that the total number of red and white marbles is 20, so

R + W = 20

We also know that the number of white marbles is 4 less than twice the number of red marbles, so

W = 2*R - 4

Now that we have defined all of the variables and setup a few equations, we can start solving for the variables.

Since we know R + W =20, and W = 2*R -4, we can use substitution to so the equation has all of the same variables.

So

R + W = 20

R + (2*R - 4) = 20

Once we have the same variables in the equation, we can now solve for R.

R + 2*R - 4 = 20

3*R - 4 = 20

3*R = 24

R = 8

So now we know there are 8 red marbles and can use this number to solve for the number of white marbles

W = 2*R - 4

W = 2*8 - 4

W = 16 -4

W = 12

So therefore we know there are 12 white marbles.

Answer 2

R is Red marble

W is White marble

W=2R-4

W+R=20+

2R-4+R=20

3R-4=20

R=8

Now substitute this into white marble equation W=2(8)-4; W=12

Number of white marbles=12

Number of red marbles=8