Hi i posted this question:
the general expression for consecutive multiples of 6 is 6N, 6(N + 1), 6(N +2), etc. find three consecutive multiples of 6 such that 4 times the first exceeds twice the third by 12.
and than Bobpursley replied:
Let N be the first, so n+1 is next, etc.
4(6(n+1))-2(6(n+3))=12
so, find n, then 6(n+1) for the first, 6(n+2) for the second, and 6(n+3) for the third.
So now i don't understand what he means by that. help me out here
Did you solve for n?
If you did, then you need three consecutive numbers divisible by six. They will be:
6(n+1) is the first number.
6(n+2) will be the second number.
You figure out what the third number will be.
Bobpursley's explanation is slightly incorrect. Let me clarify it for you.
First, let's solve the equation to find the value of N:
4(6(N+1)) - 2(6(N+3)) = 12
Multiply each term inside the parentheses:
24(N+1) - 12(N+3) = 12
Distribute the multiplication:
24N + 24 - 12N - 36 = 12
Combine like terms:
12N - 12 = 12
Add 12 to both sides:
12N = 24
Divide both sides by 12:
N = 2
Now that we have found the value of N, we can substitute it back into the expression to find the three consecutive multiples of 6:
First multiple: 6(N+1) = 6(2+1) = 6(3) = 18
Second multiple: 6(N+2) = 6(2+2) = 6(4) = 24
Third multiple: 6(N+3) = 6(2+3) = 6(5) = 30
So, the three consecutive multiples of 6 that satisfy the given conditions are 18, 24, and 30.
Yes, I can help you understand what Bobpursley meant in their response.
In the given problem, we're looking for three consecutive multiples of 6. The general expression for consecutive multiples of 6 is 6N, 6(N + 1), 6(N + 2), and so on. Here, N represents any integer.
Bobpursley suggested solving the equation: 4(6(n+1)) - 2(6(n+3)) = 12.
To solve for n, you need to simplify the equation and find the value of n that satisfies it. Once you find that value, you can use it to determine the three consecutive multiples of 6.
Let's assume you have found the value of n. For example, let's say n = 2.
To find the first consecutive multiple of 6, you substitute this value into the expression 6(N + 1): 6(2 + 1) = 6(3) = 18.
Similarly, you can find the second consecutive multiple of 6 by substituting n into the expression 6(N + 2): 6(2 + 2) = 6(4) = 24.
Finally, to find the third consecutive multiple of 6, you can substitute n into the expression 6(N + 3). In this case, it would be 6(2 + 3) = 6(5) = 30.
Therefore, the three consecutive multiples of 6, given n = 2, are 18, 24, and 30.
Make sure to substitute the actual value of n that you obtained in your calculations to find the correct set of three consecutive multiples of 6.