Three consecutive integers are such that when they are taken in increasing order and multiplied by 2,3 and 4respectively, they add up to 74. Find these numbers.
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Answer:
Three consecutive integers are such that, when they are taken in increasing order and multiplied by 2, 3, and 4, respectively, they add up to 74. How would one find these numbers?
Consecutive numbers are numbers that follow each other in order. They have a difference of 1 between every two numbers.
Let the smallest of consecutive integer be n,
Therefore, other two consecutive integers are to be n + 1 and n + 2 in increasing order
Now multiplying these three consecutive numbers with 2, 3, and 4 respectively. They become
2 (n), 3 (n + 1) and 4 (n + 2)
These add up to 74, means
2 (n) + 3 (n + 1) + 4 (n + 2) = 74
2n + 3n + 3 + 4n + 8 = 74
9n + 11 = 74
9n = 74 - 11
9n = 63
n = 63/9
n = 7
The smallest consecutive Integer is 7, therefore other two consecutive integers are:
7 + 1 = 8
7 + 2 = 9
Thus the three consecutive integers are 7, 8 and 9
Answer the three consecutive integers are 7, 8 and 9
Let the numbers be x, x + 1, x + 2.
Acc. to the question,
→ 2x + 3(x + 1) + 4(x + 2) = 74
=> 2x + 3x + 3 + 4x + 8 = 74
=> 9x + 11 = 74
=> 9x = 74 - 11
=> 9x = 63
=> x = 63/9
=> x = 7
Therefore, the numbers are :
x = 7
x + 1 = 8
x + 2 = 9