The sum of 3 consecutive even number is 71 the is number
Answers
Step-by-step explanation:
Let n = the first of three consecutive numbers.
Let n + 1 = the second consecutive number, and ...
Let n + 2 = the third consecutive number.
Since we're given that: "the sum of three consecutive numbers is 210," then we can now translate this statement mathematically into the following equation to be solved for the unknown number n:
n + (n + 1) + (n + 2) = 210
n + n + 1 + n + 2 = 210
Collecting like-terms on the left, we get:
3n + 3 = 210
3n + 3 - 3 = 210 - 3
3n + 0 = 207
3n = 207
(3n)/3 = 207/3
(3/3)n = 207/3
(1)n = 69
n = 69
Therefore, ,...
n + 1 = 69 + 1 = 70 and
n + 2 = 69 + 2 = 71
CHECK:
n + (n + 1) + (n + 2) = 210
69 + (70) + (71) = 210
69 + 70 + 71 = 210
210 = 210
Therefore, the three consecutive numbers whose sum is 210 are indeed 69, 70, and 71, and 71 is obviously the largest of these three numbers.
Answer:
Step-by-step explanation:
The actual “answer” is very easy. For two consecutive numbers, If one number is x, the other is either x + 1 or x - 1. However, that does not really answer the question using real numbers as will be done below.
First determine whether two consecutive numbers can add to the number. This can only occur with odd numbers. With even numbers, there are not consecutive numbers that can be added to equal the number.
This is an odd number, so go to the next step, subtract 1. That gives us 70. When 1 is subtracted from an odd number, we get an even number (a number divisible by 2).
Next divide 70 by 2 to get 35. That means 35 + 35 = 70.
The next step is to add 1 back to one of the 35’s. 35 + 1 = 36.
These numbers can then be added together to get the desired answer. 35 + 36 = 71.
This method of subtracting 1, dividing by 2, and adding 1 to one of the factors of 2 will work for any odd number.
To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:
X + X + 1 + X + 2 = 71
3X + 3 = 71
3X + 3 - 3 = 71 - 3
3X = 68
3X/3 = 68/3
X = 22 2/3
Since 22 2/3 is not an integer, there is no true answer to this problem.
However, there are three numbers that add up to 71. The first number is (22 2/3), the second number is (22 2/3) + 1, and the third number is (22 2/3) + 2. Therefore, we could make this the answer to "Three consecutive numbers that add up to 71 are?":
22 2/3 + 23 2/3 + 24 2/3 = 71
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