Question 36375
This is an application with the systems of equations.

Allow x to equal red chips and y to equal blue chips.

The set of equations will look like.
5x+7y=69
9x+3y=57

Multiply the top by 3 and the bottom by 7 to make the y terms the same.
15x+21y=207
63x+21y=399

Subtract and change the signs.
15x+21y=207
-63x-21y=-399

Add.
-48x=-192

Divide.
x=4

Substitute four into one of the equations.
5(4)+7y=69
20+7y=69

Subtract 20
7y=49
y=7

Since y is the blue chip the blue chip's value is $7.