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1. The sum of seven consecutive numbers is 175. What is the difference between twice the largest number and thrice the smallest number ?
Then,
⇔ x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6) = 175
⇔ 7x + 21 = 175
⇔ 7x = 154
⇔ x = 22
Required difference :
= 2(x + 6) - 3x
= 12 - x
= 12 - 22
= -10
Solution:
Let the seven numbers be x, (x + 1), (x + 2), (x + 3), (x + 4), (x + 5) and (x + 6)Then,
⇔ x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6) = 175
⇔ 7x + 21 = 175
⇔ 7x = 154
⇔ x = 22
Required difference :
= 2(x + 6) - 3x
= 12 - x
= 12 - 22
= -10