if 9 is added to twice a number and this sum is multiplied by 4, the result is the same as if the number is multiplied by 4 and 8 is added to the product. What

Question

if 9 is added to twice a number and this sum is multiplied by 4, the result is the same as if the number is multiplied by 4 and 8 is added to the product. What is the number

Answer 1

Tera,

Let's call the number we are looking for X.

 

add 9 to twice the number:  9 + 2 * X

multiply this sum by 4:  4 * (9 + 2 * X)

 

this is equal to the number multiplied by 4: 4 * X

with 8 added to the product: 8 + 4 * X

 

Now write as a single equality

4 * (9 + 2 * X) = 8 + 4 * X

 

simplify on both sides

 

4*9 + 4*2*X = 8 + 4*X

36 + 8*X = 8 + 4*X

 

subtract 36 from each side

36 + 8*X - 36 = 8 + 4*X - 36

 

reduces to

8*X = -28 + 4*X

 

subtract 4*X from each side

8*X - 4*X = -28 + 4*X - 4*X

 

reduces to

4*X = -28

 

and when we divide by 4 on both sides leaves

X = -28/4

or

X = -7

 

I hope this answers your question clearly...

-george

 

corrected after comment from Catherine, thank you for pointing out my error Catherine.