Question 388315: there are 5 questions of which I am having difficutly. Could you please help me. Thank you so much.
1.find 3 consecutive integers such as the slum of the first two equals three times the third.
2. find 2 consecutive integers such that three times the second equals 5 more than the first.
3. find 3 consecutive odd integers such that the sum of the second and the third equals 3 less than the first.
4. find 4 consecutive even integers such that the slum of the 3rd and the 4th equals 6 less than 4x the second
5. find 3 consecutive integers sulch that the slum of all 3 integers equals twice the 2nd.
Found 2 solutions by stanbon, ewatrrr:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1.find 3 consecutive integers such as the sum of the first two equals three times the third.
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1st: x-1
2nd: x
3rd: x+1
Solve: x-1 + x = 3(x+1)
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2. find 2 consecutive integers such that three times the second equals 5 more than the first.
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1st: x
2nd x+1
Solve: 3(x+1) = 5x
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3. find 3 consecutive odd integers such that the sum of the second and the third equals 3 less than the first.
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1st: 2x-1
2nd: 2x+1
3rd: 2x+3
Solve: 2x+1+2x+3 = 3(2x-1)
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4. find 4 consecutive even integers such that the sum of the 3rd and the 4th equals 6 less than 4x the second
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1st: 2x-2
2nd: 2x
3rd: 2x+2
4th: 2x+4
Solve: 2x+2 + 2x+4 = 4*2x-6
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5. find 3 consecutive integers such that
the sum of all 3 integers equals twice the 2nd.
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1st: x
2nd: x+1
3rd: x+2
Solve: x + x+1 + x+2 = 2(x+1)
3x+3 = 2x+2
x = -1
====
Cheers,
Stan H.
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Answer by ewatrrr(24785)  (Show Source):
You can put this solution on YOUR website!
Hi,
Let x, (x+1),(x+2) represent the 1st, 2nd and 3rd consecutive integers(differ by 1),
for ex, then proceeding to Write as we Read
the sum of the first two equals three times the third.
1. x + (x+1) = 3(x+2)
three times the second equals 5 more than the first
2. (2 consecutive integers) 3(x+1) = x +5
sum of all 3 integers equals twice the 2nd
5. x + (x+1) + (x+2)= 2(x+1)
Odd or even consecutive integers differ by 2
Let x, (x+2), (x+4), (x+6) etc ... represent them in order
for ex, then proceeding to Write as we Read
sum of the second and the third equals 3 less than the first
3. (x+2) + (x+4) = x -3
sum of the 3rd and the 4th equals 6 less than 4x the second
4. (x+4) + (x+6) = 4(x+2)-6
solving for x in ease case, will result in naming the integers
1. x + (x+1) = 3(x+2)
2x + 1 = 3x + 6
-5 = x Integers are -5,-4,-3
2. 3(x+1) = x+5
3x + 3 = x + 5
2x = 2
x = 1 Integers are 1,2,3
Will leave the rest to for You. Always recommend checking your answers.
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