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The sum of three consecutive odd

numbers is 45.
a) If the middle one is m - 1. Find the
numbers.
(Show working)

User RoryG
by
8.4k points

1 Answer

3 votes

Answer:

13, 15, 17 are the three consecutive odd numbers.

Explanation:

Consecutive odd numbers are separated from the preceding and succeeding ones by a value of 2

For example, 1, 3 and 5 are three consecutive numbers and the difference between successive numbers is 2

If m - 1 is the middle integer

then the first integer = (m-1) - 2 = m-3

The third integer = (m - 1) + 2 = m + 1

It is given that the sum of the three consecutive odd integers is 45

So (m - 3) + (m - 1) + (m + 1) = 45

Expanding the brackets
m - 3 + m - 1 + m + 1 = 45

Grouping like terms

m + m + m -3 -1 + 1 = 45

3m - 3 = 45

3m = 45 + 3 = 48

m = 48/3 = 16

So the three integers are
m - 3 = 16 - 3 = 13

m -1 = 16 - 1 = 15

m + 1 = 16 + 1 = 17

13, 15 and 17 are the three consecutive odd integers

Sidenote

An alternate approach is to realize that the middle number in a set of 3 consecutive numbers is the average = total/3 = 45/3 = 15

So the middle number is 15, the first number is 15 - 2 = 13 and the last number is 15+2 = 17


Choose whichever method of solution is easier for you to understand

User ChristopheCVB
by
7.2k points

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