Hi Susie.

I think I would infer parentheses (brackets) into the sentence this way:

(The product of a number and 9) increased by 15 is the same as (one half) of [the difference of eight and (four times the number)].

Let's call the number we are trying to find "n". Now we can turn the sentence into a mathematical equation using BEDMAS:

Brackets:
"(The product of a number and 9)" means (9n).

"(four times a number)" means (4n).

so "[the difference of eight and (four times the number)]" means (8 - 4n).

Now we have this:
9n increased by 15 is the same as (one half of) (8 - 4n).

Exponents: none.
Division: none.

Multiplication:
"one half of" means 0.5 times.

Addition:
"increased by 15" means + 15.

Subtraction: none left.

Finally, "is the same as" means =.

So we have translated the sentence to this:

9n + 15 = 0.5 (8 - 4n)

Can you do the algebra part now?

Hope this helps,
Stephen La Rocque.