can someone check if i got this right.?

Question

five consecutive integers have a sum of 80. find the least of these integers.

a.18
b.16
c.15
d.14
e.12

my answer is e.12, if i got it wrng can someone explain why?

Answer 1

There's an algebraic way to do this.
Consecutive integers means that each subsequent integer is greater than the previous by 1.
So, if x is your original integer, then a list of five consecutive integers is:
x, x + 1, x + 2, x + 3, x + 4

Where x + 2 = (x + 1) + 1. . .so it's one more than the previous integer.

Anyway, since you know all the integers, you can write an equation:
x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 80

Rearrange so that all the x's and all the integers are grouped:
(x + x + x + x + x) + (1 + 2 + 3 + 4) = 80
5x + 10 = 80
Now, take the 10 over to the right:
5x + 10 - 10 = 80 - 10
5x = 70
Divide both sides by 5
x = 14

So, the answer should be D.
Use algebra! If that doesn't work, try adding them up. Here's why E is wrong:
12 + 13 + 14 + 15 + 16 = 70
which does not equal 80

Answer 2

To solve this use x+x+1+x+2+x+3+x+4=80 or 5x+10=80. x=14. Therefore the set of integers is 14,15,16,17,18. D is the correct answer. As for the equation, you have the least number, x. Since there are five other numbers and they are consecutive (they go in order, although you already know this, I'm sure) you add 1 to x each time. Then, all that equals 80, so you get the equation above. Hope this helps.

Answer 3

14 +15 +16 +17 +18=80
Least would be 14. You left out the 17 (so 16 and 18 are not consecutive numbers. You also left out the 13.)

Answer 4

Start with 12 (supposedly the lowest), and add 13, 14, 15 and 16 to it. You get 70, not 80. In a problem like this you can always check your answer this way.

Answer 5

5 consecutive integers.
Let the first one be described as "x", the next one as "x+1", the next one by "x+2", the fourth one as "x+3", and the fifth one as "x+4".

The summation of these 5 integers should be 80, so

1st integer + 2nd integer + 3rd integer + 4th integer + 5th integer = 80, or
(x) + (x+1) + (x+2) + (x+3) + (x+4) = 80 (Substitution)
5x + 10 = 80 (Addition)
5x = 70 (Subtract 10 from both sides)
x = 14 (Divide both sides by 5)

Because X is your smallest integer, x = 14.

Answer 6

because 12+13+14+15+16= 70
the correct answer is 14 because 14+15+16+17+18=80

Answer 7

x, x + 1, x + 2, x + 3, and x + 4

x + x + 1 + x + 2 + x + 3 + x + 4 = 80
5x + 10 = 80
5x = 70
x = 14

the least number is 14