SOLUTION: find five consecutive odd integers such that the sum of the first and the fifth is one less than three times the fourth. i need help understanding consecutive numbers..please.

Question 96093This question is from textbook prentice hall mathematics algebra 1
: find five consecutive odd integers such that the sum of the first and the fifth is one less than three times the fourth.
i need help understanding consecutive numbers..please.
THanks! This question is from textbook prentice hall mathematics algebra 1

Found 2 solutions by checkley71, bucky:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
consecutive numbers are represented by:
x,(x+2),(x+4),(x+6) & (x+8)
x+(x+8)=3(x+6)-1
x+x+8=3x+18-1
2x-3x=17-8
-x=9
x=-9 answer for the first number
-9+2=-7 second number
-9+4=-5 third number
-9+6=-3 fourth number
-9+8=-1 fifth number
proof
-9+(-1)=3*-3-1
-10=-9-1
-10=-10

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Consecutive numbers are numbers that come one right after another. For example, 7, 8, 9, 10, 11,
and so on are consecutive numbers. Notice that if x is an unknown number, the next consecutive
number is x + 1. And the next consecutive number is x + 2, then x + 3 and so on.
.
However, consecutive odd numbers are 2 numbers apart. As an example 7, 9, 11, 13, 15, and so on
are consecutive odd numbers. If the first odd number is x, then the next consecutive odd
number is x + 2 and the next consecutive odd number is x + 4 followed by x + 6 and so on.
In the example, x was 7. It was followed by x + 2 (7 + 2) and was 9. It was followed by
x + 4 (7 + 4) and was 11. (This presumes that you know an odd number is a number that does
not have just an integer as an answer when you divide it by 2.)
.
Consecutive even numbers work just like consecutive odd numbers. An example of consecutive
even numbers is 6, 8, 10, 12, 14, 16 and on and on. If the first even number is x, then the
next consecutive even number is x + 2, and the one after that is x + 4 followed by x + 6
etc. (Again this presumes that you know an even number is one that produces an integer as
the answer when you divide it by 2.)
.
The problem tells you to find 5 consecutive odd numbers. Let x be the first one. Then the
second one is x + 2, the third one x + 4, the fourth one x + 6, and the fifth one x + 8.
.
The problem says that the sum of the first and the fifth is one less than the three times
the fourth. So if you add the first and the fifth and then add 1 to that the result should
equal 3 times the fourth. In equation form this is:
.
x + x + 8 + 1 = 3(x + 6)
.
Add the x terms and the number terms on the left side and the equation becomes:
.
2x + 9 = 3(x + 6)
.
Multiply out the right side by multiplying 3 times each of the terms in the set of parentheses
to get:
.
2x + 9 = 3x + 18
.
Subtract 3x from both sides to get rid of the 3x on the right side. The result of this
subtraction is that the equation is reduced to:
.
-x + 9 = 18
.
Subtract 9 from both sides to get rid of the 9 on the left side and the equation becomes:
.
-x = 9
.
But we are trying to solve for x, not for -x. So change the left side to +x by multiplying both
sides by -1 to get:
.
x = -9
.
Now we know that the first odd integer (we said it was x) is -9
.
The second consecutive odd number is -9 + 2 = -7
.
The third consecutive odd number is -9 + 4 = -5
.
The fourth consecutive odd number is -9 + 6 = -3
.
And the fifth and final consecutive odd number is -9 + 8 = -1
.
Now let's check the problem find the sum of the first and the fifth. This sum is -9 + (-1)
and this equals -10. Next find three times the fourth which is 3 times -3 = -9.
Now ask yourself,
is -10 actually 1 less than -9. Yes it is, because -10 is one unit to the LEFT of -9 on
the number line. Therefore, our answer checks. The five consecutive odd numbers that satisfy
the conditions of the problem are -9, -7, -5, -3, and -1.
.
Hope this helps you to understand consecutive numbers, consecutive odd numbers, and consecutive
even numbers ... as well as understanding how to solve this problem.
.

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