A bag contains green marbles and blue marbles, 68 total. The number of green marbles is 2 less than 4 times the number of blue marbles. How many green marbles are there?

There are 54 green marbles.

Step-by-step explanation:

Make two equations and you are going to solve them like systems of equations. Have x=green marbles and y=blue marbles.

x + y = 68

x = 4y - 2

Since we are finding the green marbles, we need to solve for x.

Rewrite the second equation: (x + 2) / 4 = y

Solve the systems with the rewritten equation.

x + (x + 2) / 4 = 68

x/1 + (x+2) / 4 = 68

4x/4 + (x+2) / 4 = 68

(4x + x + 2) / 4 = 68

(5x + 2) / 4 = 68/1

Cross multiply

5x + 2 = 68 (4)

5x + 2 = 272

5x = 270

x = 54

You can find the blue marbles just to check your work.

(4y - 2) + y = 68

5y - 2 = 68

5y = 70

y = 14

54 (green marbles) + 14 (blue marbles) = 68