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Three whole numbers a, b and c satisfy the equations a*(b+c)= 26 and (a+C)*b=50. If a, b and c are each between 1 and 9 inclusive , find their values

User Derek Fung
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1 Answer

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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.

User Fission
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