Question

Alice spent 6 minutes on each factoring problem and 3 minutes on each evaluation problem. she spent a total of 42 minutes on 9 problems. how many minutes did she spend on factoring?

Answer 1

let
x------> number of factoring problem
y------> number of evaluation problem

we know that
x+y=9------> multiply by -6------> -6x-6y=-54-----> equation 1
6x+3y=42------> equation 2

adds equation 1 and equation 2

-6x-6y=-54
6x+3y=42
------------------
-6y+3y=-54+42-------> -3y=-12----------> y=4
x+y=9--------> x=9-y-----> x=9-4-----> x=5

she spend on factoring------> 6x-----> 6*5-----> 30 minutes

the answer is
30 minutes