Question

Five times the sum of a number and 3 is the same as 3 multiplied by 1 less than twice the number. What is the number?

Answer 1

Let the unknown number be denoted as \( x \).

According to the problem, five times the sum of the number and 3 can be expressed as:

\[
5(x + 3)
\]

Three times 1 less than twice the number can be expressed as:

\[
3(2x - 1)
\]

Setting these two expressions equal gives the equation:

\[
5(x + 3) = 3(2x - 1)
\]

Now, we will simplify both sides.

First, simplify the left side:

\[
5(x + 3) = 5x + 15
\]

Next, simplify the right side:

\[
3(2x - 1) = 6x - 3
\]

Now we have the equation:

\[
5x + 15 = 6x - 3
\]

To isolate \( x \), subtract \( 5x \) from both sides:

\[
15 = 6x - 5x - 3
\]

This simplifies to:

\[
15 = x - 3
\]

Now, add 3 to both sides:

\[
15 + 3 = x
\]

So we find:

\[
x = 18
\]

Thus, the number is \( \boxed{18} \).

To verify, we can substitute back into the original conditions of the problem:

- The left side:
\[
5(18 + 3) = 5 \times 21 = 105
\]
- The right side:
\[
3(2 \times 18 - 1) = 3(36 - 1) = 3 \times 35 = 105
\]

Both sides are equal, confirming that the solution is correct. The number is indeed \( \boxed{18} \).