If the first even number is 'd' , then next 3 consecutive even numbers are ____________
Answers
Answer:
d+1,d+2,d+3
Step-by-step explanation:
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Answer:
Let 2n = the smallest consecutive even number.
Let 2(n + 1) = 2n + 2 = the next consecutive even number, and ...
Let 2(n + 2) = 2n + 4 = the third consecutive even number.
Since the sum of these 3 consecutive even numbers is 60, we can write the following equation:
2n + (2n + 2) + (2n + 4) = 60
2n + 2n + 2 + 2n + 4 = 60
By the Commutative Property of Addition, i.e., a + b = b + a, we have on the left side of the equation:
2n + 2n + 2n + 2 + 4 = 60
Now, collecting like-terms on the left side, we get:
(2 + 2 + 2)n + 6 = 60
(6)n + 6 = 60
6n + 6 = 60
Now, in order to solve for n, we begin isolating n on the left side of the equation by subtracting 6 from both sides:
6n + 6 - 6 = 60 - 6
6n + 0 = 54
6n = 54
Now, finish solving for n by dividing both sides by 6:
(6n)/6 = 54/6
(6/6)n = 54/6
(1)n = 9
n = 9
Therefore, the smallest consecutive even number is:
2n = 2(9)
2n = 18
CHECK:
2n + (2n + 2) + (2n + 4) = 60
2n + 2n + 2 + 2n + 4 = 60
2(9) + 2(9) + 2 + 2(9) + 4 = 60
18 + 18 + 2 + 18 + 4 = 60
36 + 2 + 18 + 4 = 60
56 + 4 = 60
60 = 60
Therefore, the smallest consecutive even number is indeed 18.
Step-by-step explanation:
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