let

x = the number of questions answered correctly by Rachel and Monica

y = the number of questions answered correctly by Joey and Chandler

Rachel and Monica have a 2:3 ratio in answering questions correctly:

x : y = 2 : 3 cross-multiply

3x = 2y

the four of them have answered correctly a total of 35 questions:

x + y = 35

by solving the system of equations:

2y = 3x

x + y = 35

we find:

x = 14 questions

y = 21 questions

click here to see the step by step solution of the system of equations:

Rachel and Monica answered 14 questions correctly.

Joey and Chandler answered 21 questions correctly.