Sum of 8numbers is X,sum of a different set of nine numbers is 2x.average of smaller set of numbers is one more than average of the larger set of numbers.write an equation for X and solve it

x/8 = 2x/9 + 1

I get 10x = 16 x ,then wat to do,lease explain,thanks

1

To find the equation for X, we need to set up two equations based on the information given and then solve them.

Let's assume the smaller set of numbers has an average of "a" and the larger set of numbers has an average of "b."

First equation:
The sum of 8 numbers is X, so we can express it as 8a. Therefore, the first equation is:
8a = X

Second equation:
The sum of a different set of nine numbers is 2X, so we can express it as 9b. Therefore, the second equation is:
9b = 2X

Now, we are given that the average of the smaller set of numbers is one more than the average of the larger set. Mathematically, we can write this as:
a = b + 1

To solve this system of equations, we can substitute the value of X from the first equation into the second equation:

9b = 2(8a)
9b = 16a

Now, substitute the value of "a" from the third equation into the above equation:

9b = 16(b + 1)
9b = 16b + 16

Simplify the equation:
16b - 9b = 16
7b = 16

Now, solve for "b":
b = 16/7

To find "a," substitute the value of "b" back into the third equation:
a = b + 1
a = (16/7) + 1
a = 23/7

Finally, substitute the values of "a" and "b" into the first equation to find X:
8a = X
8(23/7) = X
184/7 = X

Therefore, the equation for X is:
X = 184/7, which simplifies to X = 26.286