Question

One more than one-half a number is the quotient of 22 less than twice the number and 3.

Answer 1

Let's denote the number as \( x \).

According to the problem, "one more than one-half a number" can be expressed as:

\[
\frac{1}{2}x + 1
\]

The phrase "the quotient of 22 less than twice the number and 3" can be expressed as:

\[
\frac{2x - 22}{3}
\]

Now we can set these two expressions equal to each other:

\[
\frac{1}{2}x + 1 = \frac{2x - 22}{3}
\]

To eliminate the fractions, we can multiply both sides of the equation by 6 (which is the least common multiple of 2 and 3):

\[
6\left(\frac{1}{2}x + 1\right) = 6\left(\frac{2x - 22}{3}\right)
\]

Simplifying both sides gives:

\[
3x + 6 = 4(2x - 22)
\]

Expanding the right-hand side:

\[
3x + 6 = 8x - 88
\]

Now, we'll rearrange the equation to isolate \( x \):

\[
3x + 6 + 88 = 8x
\]

\[
94 = 8x - 3x
\]

\[
94 = 5x
\]

Now, divide by 5:

\[
x = \frac{94}{5}
\]

Thus, the solution is:

\[
x = 18.8
\]

So the number is \( \frac{94}{5} \) or \( 18.8 \).