Write a system of equations to represent the situation and solve. Define your variables.

Question

There are 27 red or blue marbles in a bag. The number of red marbles is 5 less than 3 times the number of blue marbles. How many red marbles are in the bag? How many blue marbles are in the bag? Show your work.

Answer 1

Recognize that 27 = total number of marbles. Let x = number of blue marbles, since red is defined in relation to blue. Therefore, 3x-5= number of red marbles. Then, total number of marbles is blue + red. Therefore, x+3x-5 = 27. 

 

Solving,

 

4x-5 = 27 add five to both sides

4x =32 divide by 4

x = 8 = blue marbles

 

3x-5 = 19 = red marbles.