If 7 times a number is decreased by 12, the result is the same as when 14 is subtracted from 8 times the number. what's the number

Question

If 7 times a number is decreased by 12, the result is the same as when 14 is subtracted from 8 times the number. what's the number

Answer 1

Hi Olivier,

 

The trick with this question is to turn all those words into an algebraic equation.   After that, you just solve for the variable.

 

Let's call the number "n."  So, one step at a time:

 

1)  "If 7 times a number"  means "7n"

2)  "is decreased by 12" means "- 12," so now it's "7n - 12"

3)  "the result is the same as"  means "=" so now we have "7n - 12 ="

4)  "when 14 is subtracted from 8 times the number"  means "8n - 14"--and this is trickier, 'cuz you have to realize the - 14 comes AFTER the 8n in the equation, because it's "subtracted FROM," even though it comes first in the words.

5)  So, all together it's:  "7n - 12 = 8n - 14"

6)  Now, we do the algebra:

7)  7n ( - 7n) - 12 = 8n (- 7n) - 14

8)   -12 = n - 14

9)  2 = n

 

That seems right, but let's check against our original equation:

 

7(2) - 12 = 8(2) - 14

14 - 12 = 16 - 14

2 = 2

 

Got it!