Question

If 18 is added to a certain number and sum

Answer 1

We are given that 18 is added to a number. If the number is "n", then we can write this mathematically as:

$n+18$

We are also given that the result is divided by 6. This is written as:

$\frac{n+18}{6}$

Now, we are given that the result is equal to 1/4 of the number plus 1, this is written as:

$\frac{n+18}{6}=\frac{1}{4}n+1$

Now, to determine the number we will solve for "n". First, we will distribute the denominator of the fraction on the left:

$\frac{1}{6}n+\frac{18}{6}=\frac{1}{4}n+1$

Now, we subtract n/4 from both sides:

$\frac{1}{6}n-\frac{1}{4}n+\frac{18}{6}=\frac{1}{4}n-\frac{1}{4}n+1$

Solving the operations:

$-\frac{1}{12}n+\frac{18}{6}=1$

Now, we simplify the fraction on the left side:

$-\frac{1}{12}n+3=1$

Now, we subtract 3 from both sides:

$-\frac{1}{12}n+3-3=1-3$

Solving the operations:

$-\frac{1}{12}n=-2$

Now, we multiply both sides by -12:

$\begin{gathered} n=(-2)(-12) \\ n=24 \end{gathered}$

Therefore, the number is 24.