Find the largest of three numbers in arithmetic progression whose sum is 87 and whose product is 24273Options15192931
Question
Find the largest of three numbers in arithmetic progression whose sum is 87 and whose product is 24273
Options:
- 15
- 19
- 29
- 31
Solution
The three numbers in an arithmetic progression can be represented as (a - d), a, and (a + d), where a is the middle term and d is the common difference.
Given that the sum of the three numbers is 87, we can write the equation:
(a - d) + a + (a + d) = 87 3a = 87 a = 87 / 3 a = 29
Given that the product of the three numbers is 24273, we can write the equation:
(a - d) * a * (a + d) = 24273 29^3 - d^2 * 29 = 24273 24389 - 29d^2 = 24273 29d^2 = 24389 - 24273 29d^2 = 116 d^2 = 116 / 29 d^2 = 4 d = ±2
Therefore, the three numbers are 27, 29, and 31. The largest number is 31.
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