X=8
Set up proportions would give you: 10/3x+1 = 22/7x-1
With that in mind, cross multiply, which would give you: 10(7x-1) = 22(3x+1).
Turns into: 70x -10 = 66x+22. Then just solve for x
Proof by induction
Base case:
n=1: 1*2*3=6 is obviously divisible by six.
Assumption: For every n>1 n(n+1)(n+2) is divisible by 6.
For n+1:
(n+1)(n+2)(n+3)=
(n(n+1)(n+2)+3(n+1)(n+2))
We have assumed that n(n+1)(n+2) is divisble by 6.
We now only need to prove that 3(n+1)(n+2) is divisible by 6.
If 3(n+1)(n+2) is divisible by 6, then (n+1)(n+2) must be divisible by 2.
The "cool" part about this proof.
Since n is a natural number greater than 1 we can say the following:
If n is an odd number, then n+1 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.
If n is an even number" then n+2 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.
Therefore by using the method of mathematical induction we proved that for every natural number n, n(n+1)(n+2) is divisible by 6. QED.
Answer:
At 15 weeks they will both weigh 180
Step-by-step explanation:
150 + 2w = 195 - w
2w + w = 195 - 150
3w = 45
w = 45/3
w = 15 <=== they will weigh the same at 15 weeks
150 + 2(15) = 150 + 30 = 180...and they will both weigh 180 lbs
I hope this helps you :)
