Can't set up/figure out

Question

Joey has a sack of 56 marbles. There are 3 colors of marbles in the sack: red, yellow and blue. If he has half as many red as blue marbles and eight more yellow than red marbles, how many of each color does he have in the sack? 

Answer 1

 

Let      r = # of red marbles

Let    2r = # of blue marbles ... (1/2 as many red as blue, means blue is twice the red)

Let r+8 =  # of yellow marbles ... (8 more than the red)

 

Total is 56 ... our equation is

 

   r + 2r + r + 8 = 56

   4r + 8 = 56

   4r = 56 - 8

   4r = 48

   r = 12

 

There are 12 red marbles.

There are 24 blue marbles.

There are 20 yellow marbles.

 

Answer 2

R = number of red marbles, Y = number of yellow marbles, B = number of blue marbles.

 

The balls of all three colors add to the total number of marbles: R + Y + B = 56.

There are half as many red as blue: (1/2)R = B

There are eight more yellow than red: Y = R + 8.

 

These are your three equations:

 

1)R + Y + B = 56

2)2R = B

3)Y = R + 8

 

This is a system of three equations with three variables which can be solved with substitution.

 

A)Plug equations 2 and 3 into equation 1, then solve for R.

 

B)Plug R back into equations 1 and 2 to find B and Y.