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MATH / The sum of the following seven numbers is exactly 19: a₁=2.56, a₂=2.61, a₃=2.65, a₄=2.71, a₅=2.79, a₆=2.82, a₇=2.86. Each a_(i) is approximated by some integer A_(i), for 1≤i≤7, su…

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problem

The sum of the following seven numbers is exactly 19: a1=2.56,a_1 = 2.56, a2=2.61,a_2 = 2.61, a3=2.65,a_3 = 2.65, a4=2.71,a_4 = 2.71, a5=2.79,a_5 = 2.79, a6=2.82,a_6 = 2.82, a7=2.86.a_7 = 2.86. Each aia_i is approximated by some integer Ai,A_i, for 1≤i≤7,1 \le i \le 7, such that the sum of the AiA_i's is also 19.19. Let MM be the maximum of the seven "errors" |Ai−ai|.|A_i - a_i|. What is the smallest possible value of MM?
Plain-text mathematical notation (without MathML)
The sum of the following seven numbers is exactly 19: a₁=2.56, a₂=2.61, a₃=2.65, a₄=2.71, a₅=2.79, a₆=2.82, a₇=2.86. Each a_(i) is approximated by some integer A_(i), for 1≤i≤7, such that the sum of the A_(i)'s is also 19. Let M be the maximum of the seven "errors" |A_(i)−a_(i)|. What is the smallest possible value of M?
Original LaTeX notation
The sum of the following seven numbers is exactly 19: $a_1 = 2.56,$ $a_2 = 2.61,$ $a_3 = 2.65,$ $a_4 = 2.71,$ $a_5 = 2.79,$ $a_6 = 2.82,$ $a_7 = 2.86.$ Each $a_i$ is approximated by some integer $A_i,$ for $1 \le i \le 7,$ such that the sum of the $A_i$'s is also $19.$ Let $M$ be the maximum of the seven "errors" $|A_i - a_i|.$ What is the smallest possible value of $M$?

level

Level 4

type

Intermediate Algebra

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task_id
fd05d309-151a-5438-907c-6b80aee8e94a
task_key
intermediate~5falgebra--test--fd05d309-151a-5438-907c-6b80aee8e94a
task_revision_id
1
config / split
intermediate_algebra / test

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