From the sums A+B=132, B+C=130, C+D=102, and B+D=116, what is B?

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Multiple Choice

From the sums A+B=132, B+C=130, C+D=102, and B+D=116, what is B?

Explanation:
Think about how the sums relate the variables to each other. If you subtract the second equation from the first, you get A - C = 2, so A is just 2 more than C. Subtracting the third equation from the fourth gives B - C = 14, so B is 14 more than C. Now use the relation B = C + 14 in the equation B + C = 130: (C + 14) + C = 130, which simplifies to 2C = 116, so C = 58. Then B = C + 14 = 58 + 14 = 72. A quick check confirms consistency: A = 60 and D = 44 satisfy all the given sums, including B + D = 116.

Think about how the sums relate the variables to each other. If you subtract the second equation from the first, you get A - C = 2, so A is just 2 more than C. Subtracting the third equation from the fourth gives B - C = 14, so B is 14 more than C.

Now use the relation B = C + 14 in the equation B + C = 130: (C + 14) + C = 130, which simplifies to 2C = 116, so C = 58. Then B = C + 14 = 58 + 14 = 72.

A quick check confirms consistency: A = 60 and D = 44 satisfy all the given sums, including B + D = 116.

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