Michael has $1,065.41 in his checking account. He is going to spend $466.86 on a new television, and he will spend the rest on speakers that cost $42.00 each. Which of the following inequalities would determine the maximum number of speakers, x, Michael can buy without spending more money than he has in his account?

Question

A.
$42.00x + $466.86 < $1,065.41
B.
$466.86 < $42.00x + $1,065.41
C.
$1,065.41 < $42.00x + $1,065.41
D.
$466.86 + $42.00 + x < $1,065.41

Answer 1

To determine the maximum number of speakers, \( x \), that Michael can buy without spending more money than he has in his checking account, we can set up the following inequality:

1. Start with the total amount in his checking account: $1,065.41
2. He spends $466.86 on the television, so we subtract that from his account.
3. He then spends money on speakers that cost $42.00 each, which is represented as \( 42.00x \).

The mathematical formulation will look like this:

\[ \text{Total spent on television and speakers} < \text{Total in checking account} \] which translates to:

\[ 466.86 + 42.00x < 1,065.41 \]

This matches option A:

A. \( 42.00x + 466.86 < 1,065.41 \)

So, the correct answer is A.