Question

Find average of all multiple of 5 from 267 to 572(a) 415(b) 417 (c) 420(d) 425


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Answer 1

To find the average of all multiples of 5 from 267 to 572, we need to determine the sum of all these multiples and divide it by the count of the multiples.

• First, let's find the first multiple of 5 that is greater than or equal to 267. We divide 267 by 5 and round up to the nearest whole number:
• 267 ÷ 5 = 53.4
• So, the first multiple of 5 that is greater than or equal to 267 is 53 * 5 = 265.
• Next, we find the last multiple of 5 that is less than or equal to 572. We divide 572 by 5 and round down to the nearest whole number:
• 572 ÷ 5 = 114.4
• So, the last multiple of 5 that is less than or equal to 572 is 114 * 5 = 570.
• Now we have the range of multiples of 5 from 265 to 570. To find the count of these multiples, we subtract the first multiple from the last multiple and divide by 5, and then add 1 to include both endpoints:
• Count = (570 - 265) ÷ 5 + 1 = 305 ÷ 5 + 1 = 61 + 1 = 62
• So, there are 62 multiples of 5 in the range from 267 to 572.
• To find the sum of these multiples, we can use the formula for the sum of an arithmetic series:
• Sum = (n/2) * (first term + last term)
• Sum = (62/2) * (265 + 570) = 31 * 835 = 25,885
• Finally, to find the average, we divide the sum by the count:
• Average = Sum / Count = 25,885 / 62 ≈ 417.34
• Therefore, the average of all multiples of 5 from 267 to 572 is approximately 417.34.
• The closest option to the calculated average is (b) 417.

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