word expressions

Question

Twice the difference of a number and 9 is equal to three times the sum of the number and 6

 

 

how would I find the number of this equation?

Answer 1

Kayla,

 

Let n = unknown number, then your problem states that

 

2(n - 9) = 3(n + 6), so 2n-18 = 3n +18, and n = -36 ; Now check it: 2(-45)=3(-30) so this solution works.

 

But the statement "the difference of a number and 9" could also be interpreted as (9 - n). So we get a new equation:

2(9 - n) = 3(n + 6), where 18 - 2n = 3n + 18, so n = 0 becomes the solution.  Check it: 2(9) = 3(6) so it also works.

 

Therefore, the ambiguity in the wording of the problem leads to two possible solutions: n=0 and n=-36.

 

Of course, you can interpret correctly the phrase as |n - 9|, and then this resolves into the 2 equations above since 

|n - 9| = +(n - 9) and = -(n - 9) = (9 - n). Then the sing;e formula would have been   2|n - 9| = 3(n + 6). The answers are still the same as before.