Answer: a = 4, b = 5, and c = 6.
Explanation:
To find the values of a, b, and c, we can solve the given equations step by step.
Equation 1: a*(b+c) = 26
Equation 2: (a+c)*b = 50
We know that a, b, and c are whole numbers between 1 and 9 inclusive.
Let's consider possible values for a, b, and c to satisfy both equations.
If we try a = 1, b = 2, and c = 6, we can substitute these values into the equations:
Equation 1: 1*(2+6) = 8 = 26 (not satisfied)
Equation 2: (1+6)*2 = 14 = 50 (not satisfied)
Since the given values do not satisfy both equations, we need to try other values.
If we try a = 2, b = 5, and c = 7:
Equation 1: 2*(5+7) = 24 = 26 (not satisfied)
Equation 2: (2+7)*5 = 45 = 50 (not satisfied)
Again, the given values do not satisfy both equations.
Next, let's try a = 3, b = 5, and c = 2:
Equation 1: 3*(5+2) = 21 = 26 (not satisfied)
Equation 2: (3+2)*5 = 25 = 50 (not satisfied)
The given values still do not satisfy both equations.
Continuing this process, we try a = 4, b = 5, and c = 6:
Equation 1: 4*(5+6) = 44 = 26 (not satisfied)
Equation 2: (4+6)*5 = 50 = 50 (satisfied)
Finally, we have found values that satisfy both equations: a = 4, b = 5, and c = 6.
Therefore, the values of a, b, and c are 4, 5, and 6 respectively.