If 200≤ a ≤ 400 and 600≤ b≤ 1200 , then the largest value of the quotient (b/a) is

AMC 8 1986 Problem 14

AMC8 1986 年第 14 题

比与比例★★★☆☆

200\leq a \leq 400

and

600\leq b\leq 1200

, then the largest value of the quotient

\displaystyle \frac{b}{a}

若

200\leq a \leq 400

且

600\leq b\leq 1200

，则商

\displaystyle \frac{b}{a}

的最大值是

正确答案 · Correct Answer

Solution 1

Since

a

and

b

are both positive,

\displaystyle \frac{b}{a}

is maximized if

b

is maximized and

a

is minimized. The maximum possible value of

b

is 1200 and the minimum possible value of

a

is 200. In this case,

\displaystyle \frac{b}{a} = \frac{1200}{200} = 6

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