Jim has a total of 77 red and blue marbles. The number of blue marbles is 5 more than twice the number of red marbles. How many red marbles are there?
R = red marbles
R + 2R + 5 = 77
3R + 5 = 77
3R = 72
R = 24
R + 2R + 5 = 77
3R + 5 = 77
3R = 72
R = 24
R = red marbles
To solve this problem, let's assign variables to the unknown quantities. Let's denote the number of red marbles as "R" and the number of blue marbles as "B."
According to the information given, we know that the total number of marbles is 77. Thus, we have the equation:
R + B = 77 (Equation 1)
We also know that the number of blue marbles is 5 more than twice the number of red marbles. In equation form, this can be expressed as:
B = 2R + 5 (Equation 2)
To find the number of red marbles, we need to solve the equations simultaneously. We can do this by substituting Equation 2 into Equation 1:
R + (2R + 5) = 77
3R + 5 = 77
3R = 72
R = 24
Therefore, there are 24 red marbles.