Find the number.

Question

If 8 is added to twice a number and its sum is multiplied by 5, te result is the same as if the number is multiplied by 6 and 12 is added to the product. what is the number

Answer 1

Good morning, Krystle!  Let's do this thing.

 

Let's let x = the number.  Twice a number is 2x, and adding 8 to it gives us 2x + 8.  Multiplying the sum by 5, we get 5(2x + 8).  Distributing through, 5(2x) + 5(8), we get 10x + 40.

 

If we multiply the number by 6, we get 6x.  Adding 12 gives us 6x + 12.

 

The problem tells us they are the same.  Thus, 10x + 40 = 6x + 12.  Subtracting 6x from both sides, we get 4x + 40 = 12.  Subtracting 40 from both sides, we get 4x = -28.  Dividing by 4, we get x = -7.

 

Let's check.  2(-7) + 8 = -14 + 8 = -6.  -6(5) = -30.

6(-7) + 12 = -42 + 12 = -30.  Check!

 

Hope this helps!