twice the sum of a number and 6 is equal to 3 times the difference of the number and 8. Find the number
1 answer:
In order to solve this problem, we must solve an equation.
First, we need to define our unknown.
Let's call our number "n".
So, the sum of the number and 6 is the same as saying n+6
Then we need to multiply it by 2 (since it's twice the sum)
2(n+6)
This whole thing is equal to three times of the difference of the number and 8
n-8 is equal to the difference between the number and 8, then we need to multiply it by three.
3(n-8)
now, we set both sides equal and solve
The number is 36
You might be interested in
Given:
The sum of two terms of GP is 6 and that of first four terms is
To find:
The sum of first six terms.
Solution:
We have,
Sum of first n terms of a GP is
...(i)
Putting n=2, we get
...(ii)
Putting n=4, we get
(Using (ii))
Divide both sides by 6.
Taking square root on both sides, we get
Case 1: If r is positive, then using (ii) we get
The sum of first 6 terms is
Case 2: If r is negative, then using (ii) we get
The sum of first 6 terms is
Therefore, the sum of the first six terms is 7.875.