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# the product of 3 consecutive numbers is 120. what is the second number?

steps in solving this problem?

### 4 Answers by Expert Tutors

Atef F. | Guaranteed success with high scores Guaranteed success with high scores
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4*5*6

Summer K. | Certified Elementary Teacher + ASVAB, Communications, and more!Certified Elementary Teacher + ASVAB, Co...
5.0 5.0 (1 lesson ratings) (1)
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Since they want THREE consecutive numbers, fine the cube root of 120.  This gives you 4.93... making your answer 4, 5, 6.

Hope this helped!

George C. | Humboldt State and Georgetown graduateHumboldt State and Georgetown graduate
5.0 5.0 (2 lesson ratings) (2)
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From below the polynomial for solution is x^3 + 3 x^2 + 2x = 120

synthetic division with 4

4    |1    3    2    -120

4   28    120

1   7   30                so 4 is a factor.  (x - 4)(x^2 + 7x + 30)

Solving the quadratic gives x = (-7 ± (71)^(1/2) i))/2

The only solution for 3 consecutive numbers is 4.  Obviously the second number in succession is 5

Sheila M. | Friendly College Math Professor - understands students' math anxietyFriendly College Math Professor - unders...
4.9 4.9 (63 lesson ratings) (63)
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Hi, Donald.

The key to solving word problems is understanding the vocabulary.  The word product means the answer from multiplying.  The word consecutive means "in a row."  So start off by setting up expressions to represent the three consecutive numbers:

first number = x
second number = x + 1
third number = x + 2

The product of these three is: x (x+1)(x+2)

Set that expression = 120, and you're ready to solve.

x(x+1)(x+2) = 120

Multiplying the three factors in our expression,
you should arrive at:  x^3 + 3 x^2 + 2x

So we have x^3 + 3 x^2 + 2x = 120
Subtract 120:  x^3 + 3 x^2 + 2x - 120 = 0

Use Synthetic Division to try out factors of neg 120.  Pos 4 works...

So we have (x- 4)(x^2 + 7x + 30) = 0
Setting each of these factors equal to zero, we have x = 4 and something else a little more challenging.  But if we stick with whole numbers, the three consecutive numbers would be 4, 5, and 6.

I am wondering...
Perhaps you copied the problem incorrectly.
Should the word, product, be the word, sum?

If that be the case, then we would add our three numbers together to get 120.
The equation would look like this:
x + (x+1) + (x+2) = 120

Combining like terms, you would have: 3x + 3 = 120
After solving this, I get x = 39.  This does NOT answer the question posed because the problem asked for the second number.  Remember we said that the first number was represented by x.  Recall that the expression representing the second number is x + 1.

Hope this helped you.