Question

A number is doubled and then 1 is added to it. The answer is divided by 5 and then increased by 16. The final result is 18.

Answer 1

A.

So let's break down this sentence (Let n = unknown number):

• "A number is doubled and then 1 is added to it"; Remember that double means multiplied by 2. With this sentence, we can determine that "2n + 1" is a part of the equation.
• "The answer is divided by 5, and then increased by 16"; The "answer" they refer to is "2n + 1" from the prior sentence. Since this is divided by 5 and then added by 16, we can determine that $\frac{2n+1}{5}+16$ is a part of our equation.
• "The final result is 18"; This means that the prior part of the equation is equal (=) to 18. With this info, our full equation is $\frac{2n+1}{5}+16=18$

B.

Now, let's solve our prior equation found in A. To solve for the unknown number, n, we need to isolate the variable onto 1 side of the equation. Firstly subtract both sides by 16 to cancel out the + 16 on the left side:

$\frac{2n+1}{5}=2$

Next, multiply both sides by 5 to cancel out the division on the left side:

$2n+1=10$

Next, subtract both sides by 1 to cancel out the + 1:

$2n=9$

Lastly, divide both sides by 2 to cancel out the multiplication:

$n=\frac{9}{2}\ \textsf{OR}\ 4.5$

In short, the number is 9/2 or 4.5.