find the number

Question

Two times the sum of some number plus 5 is equal to 9 times the difference of the number and 2. Find the number.

Answer 1

Hello Jennifer

 

Let 'n' = number

 

2 times the sum of n + 5 = 9 times the difference of n -2

 

2(n+5) = 9(n-2)

 

2n + 10 = 9n - 18

 

9n - 2n = 10 + 18

 

7n = 28

 

Therefore, n = 4.

 

To verify if this is true, plug in n = 4 into the above equation

 

2(n+5) = 9(n-2)

 

2(4+5) = 9(4-2)

 

2(9) = 9(2)

 

18 = 18

Answer 2

Ok. So you need to write the problem in the form of an equation:

 

Let's call the number (X)

two times the sum (addition) of some number plus 5

so,

2(X + 5) =  9 times the difference (subtraction) of the number and 2 

2(X + 5) = 9(X - 2)

Now, we solve for X

2X + 10 = 9X - 18

subtract 2X from both sides:

10 = 7X - 18

28 = 7X

28/7 = X = 4

 

So the number is 4