Four people A, B, C, D on a scale give sums A+B=132, B+C=130, C+D=102, B+D=116. What is D's weight?

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Multiple Choice

Four people A, B, C, D on a scale give sums A+B=132, B+C=130, C+D=102, B+D=116. What is D's weight?

Explanation:
Use the given sums to relate the weights and eliminate variables. Look at the two sums that share B: B+C = 130 and B+D = 116. Subtracting the second from the first gives C − D = 14, so D = C − 14. Now use the sum C + D = 102 and substitute D = C − 14: C + (C − 14) = 102, which simplifies to 2C = 116, so C = 58. Therefore D = C − 14 = 44.

Use the given sums to relate the weights and eliminate variables. Look at the two sums that share B: B+C = 130 and B+D = 116. Subtracting the second from the first gives C − D = 14, so D = C − 14. Now use the sum C + D = 102 and substitute D = C − 14: C + (C − 14) = 102, which simplifies to 2C = 116, so C = 58. Therefore D = C − 14 = 44.

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