Question

Candidate A and Candidate B are running for mayor. A poll was taken to determine which candidate would likely win the election. The poll is accurate within ±5%. Write an absolute value equation to find the maximum and minimum percentage of voters who will vote for Candidate A if 38% of the voters in the poll voted for Candidate A. Let A represent the percent of voters who will vote for Candidate A.

Answer 1

`|A-38|=5`

33% or 43%

Explanation:

Given that poll is accurate within
`\pm5`.

38% voters have voted for candidate A.

`A` is the percent of voters who will vote for candidate A.

So, value of A can be 38+5=43%

OR

38-5 = 33%

We will write an absolute function for the above situation.

But, first of all, let us have a look at the definition of Absolute value function.

`|y|=\left \{ {-{y}\ if\ y<0 \atop {y}\ if\ y>0} \right.`

The the value of function gives us a negative sign when the value inside the modulus function is negative.

`A-38` will be negative when
`A < 38` and

`A-38` will be positive when
`A>38`.

This difference is given as
`\pm5`.

Therefore, the absolute value function can be written as:

`|A-38|=5`

Case 1:
`A < 38`

As per definition of modulus function, it will open with a negative sign.

`-A+38=5\Rightarrow A = 33`

Case 2:
`A>38`

As per definition of modulus function, it will open with a positive sign.

`A-38=5\Rightarrow A = 43`

Therefore the answer is 33% or 43%