Question

9/10 times a number plus 6 is 51

Answer 1

So,

Let's translate this into mathematical form.
"9/10 times a number"
$\frac{9}{10} n$

"plus 6 is 51"
+ 6 = 51

So we have our equation:
$\frac{9}{10} n + 6 = 51$

Subtract 6 from both sides.
$\frac{9}{10} n = 45$

Multiply both sides by the reciprocal of 9/10 (10/9).
$n = (45) \frac{10}{9}$

Multiply.
$\frac{45}{1} * \frac{10}{9} --\ \textgreater \ \frac{5}{1} * \frac{10}{1} = 50$

The number is 50.

Check.
$\frac{9}{10} * 50 + 6 = 51$

Multiply.
$45 + 6 = 51$

Add.
$51 = 51$
This checks.

S = {50}

Answer 2

N = the number

9/10n + 6 = 51                                       Original Problem.
9/10n = 46                                            Subtract 6 from each side.
n = 51.11111111111111111111                  Multiply each side by (10/9)

Answer: n = 51.111111111111111111111