To solve this problem, we can use a system of two equations with two unknowns, based on the information given.
Let x be the part of A that varies with B, and y be the part of A that varies with C. Then we have:
A = xB + yC
Using the values given in the problem, we can write two equations:
When B = 2 and A = 28:
28 = 2x + 0y (since C is not mentioned)
When B = 3 and C = 26 and A = 12:
12 = 3x + 26y
Now we can solve for x and y by solving the system of equations:
2x = 28 => x = 14
3x + 26y = 12 => 42 + 26y = 12 => 26y = -30 => y = -15/13
Therefore, we have:
A = 14B - 15/13C
a) To find the value of A when B=4 and C=6, we can substitute B=4 and C=6 into the equation:
A = 14(4) - 15/13(6) = 56 - 45/13 = 383/13
Therefore, A is equal to 383/13 when B=4 and C=6.
b) To find the value of B when A=38 and C=6, we can rearrange the equation to solve for B:
A = 14B - 15/13C => 13A = 182B - 15C => 13A + 15C = 182B
Substituting A=38 and C=6, we have:
13(38) + 15(6) = 182B => 494 = 182B => B = 247/91
Therefore, B is equal to 247/91 when A=38 and C=6.