A shipping clerk has five boxes of different but unknown weights each weighing less than 100 kg. The clerk weights the boxes in pairs. The weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121 kg. What is the weight of the heaviest box?
Answers
Answer:
Explanation:
=> Suppose, the weight of the five boxes with the shipping clerk is p, q, r, s and t.
where, p ≤ q ≤ r ≤ s ≤ t.
110 = p + q < p + r < ... < r + t < s + t = 121
e.g. p + r = 112 and r + t = 120
=> Here, each box is weighed four times.
Thus, 4p + 4q + 4r + 4s + 4t = 110 + 112 + 113 + 114 + 115 + 116 + 117 + 118 + 120 + 121
4 (p + q + r + s + t) = 1156
p + q + r + s + t = 1156/4
p + q + r + s + t = 289
=> that means, p + q = 110 and s + t = 121
∴ 110 + r + 121 = 289
∴ r = 289 - 231
r = 58
=> place this value in r + t = 120
58 + t = 120
t = 120 - 58
t = 62 kg.
Thus, the weight of the heaviest box is 62 kg.
Answer:Let the weight of the five boxes with the shipping clerk is p, q, r, s and t.
where, p ≤ q ≤ r ≤ s ≤ t.
110 = p + q < p + r < ... < r + t < s + t = 121
e.g. p + r = 112 and r + t = 120
= Here, each box is weighed four times.
Thus, 4p + 4q + 4r + 4s + 4t = 110 + 112 + 113 + 114 + 115 + 116 + 117 + 118 + 120 + 121
4 (p + q + r + s + t) = 1156
p + q + r + s + t = 1156/4
p + q + r + s + t = 289
= that means, p + q = 110 and s + t = 121
∴ 110 + r + 121 = 289
∴ r = 289 - 231
r = 58
= place this value in r + t = 120
58 + t = 120
t = 120 - 58
t = 62 kg. Ans...
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Explanation: