SAT Math help » Arithmetic » Integers » order » continuous Integers » just how to uncover consecutive integers
Explanation:

Three consecutive also integers deserve to be represented by x, x+2, x+4. The amount is 3x+6, i beg your pardon is same to 108. Thus, 3x+6=108. Fixing for x returns x=34. However, the concern asks because that the largest number, i m sorry is x+4 or 38. Please make certain to prize what the concern asks for!

You can have likewise plugged in the price choices. If you plugged in 38 as the largest number, then the previous also integer would certainly be 36 and the following previous also integer 34. The sum of 34, 36, and also 38 returns 108.

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### Example concern #1 : just how To uncover Consecutive Integers

The amount of 3 consecutive also integers equals 72. What is the product of this integers?

10560

12144

13800

17472

13728

13728

Explanation:

Let us call x the the smallest integer. Since the next two numbers are consecutive even integers, us can speak to represent them together x + 2 and x + 4. We space told the sum of x, x+2, and x+4 is same to 72.

x + (x + 2) + (x + 4) = 72

3x + 6 = 72

3x = 66

x = 22.

This method that the integers space 22, 24, and 26. The concern asks us for the product of these numbers, i beg your pardon is 22(24)(26) = 13728.

The prize is 13728.

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### Example concern #1 : how To discover Consecutive Integers

Four continually integers have actually a median of 9.5. What is the biggest of these integers?

13

12

9

11

8

11

Explanation:

Four continuous integers can be represented as n, n+1, n+2, n+3

Therefore, by saying that they have a average of 9.5, we median to say:

(n + n+1 + n+2 + n+ 3)/4 = 9.5

(4n + 6)/4 = 9.5 → 4n + 6 = 38 → 4n = 32 → n = 8

Therefore, the biggest value is n + 3, or 11.

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### Example question #4 : just how To discover Consecutive Integers

The amount of 4 consecutive odd integers is equal to 96. How countless of the integers are prime?

1

0

4

2

3

1

Explanation:

Let x be the the smallest of the four integers. We room told that the integers space consecutive weird integers. Due to the fact that odd integers space separated by two, each consecutive odd creature is two bigger than the one prior to it. Thus, we can let + 2 represent the second integer, + 4 stand for the third, and also + 6 represent the fourth. The sum of the four integers equals 96, therefore we can write the complying with equation:

x + (+ 2) + (+ 4) + (+ 6) = 96

Combine x terms.

4x + 2 + 4 + 6 = 96

Combine constants ~ above the left side.

4x + 12 = 96

Subtract 12 native both sides.

4x = 84

Divide both sides by 4.

x = 21

This method the smallest integer is 21. The other integers are therefore 23, 25, and 27.

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The concern asks united state how countless of the four integers room prime. A prime number is divisible just by itself and one. Among the 4 integers, only 23 is prime. The number 21 is divisible by 3 and 7; the number 25 is divisible by 5; and also 27 is divisible by 3 and 9. Thus, 23 is the only number indigenous the integers that is prime. There is only one element integer.