Question

Michael has $1,024.55 in his checking account. He is going to spend $536.89 on a new television and spend the rest on speakers that cost $47.00 each. Which of the following inequalities would determine the maximum number of speakers (y) Michael can buy without spending more money than is in his account? pls help ASAP! the choices are

A.

$1,024.55 < $47.00(y) + $1,024.55

B.

$1,024.55 + $536.89 > $47.00 + y

C.

$536.89 + $47.00(y) < $1,024.55

D.

$536.89 < $47.00(y) + $1,024.55

Answer 1

C. $536.89 + $47.00(y) < $1,024.55

Explanation:

We know that Michael wants to spend no more than $1024.55. Therefore, we use the inequality given in C to find the maximum number of speakers he could buy without exceeding $1,024.55.

Another way to solve with the information if 47(y) < $1,024.55 - $536.89, but since this isn't one of the answer choices, C. is the answer.

Optional Step: We can see how the inequality works by solving for y.

1. Subtract 536.89 from both sides:

(536.89 + 47.00(y) < 1024.55) - 536.89

47(y) < 487.66

2. Divide both sides by 47 to find the maximum number of speakers Michael could buy without exceeding $1,024.55:

(47(y) < 487.66) / 47

y < 10.3757

y < 10

Because you can't have part of a speaker, the answer is 10.

If we were to plug in 10 or any other number less than for y, we'd get a number less than 1024.55, which shows that the inequality works:

47(10) + 536.89 < 1024.55

470 + 536.89 < 1024.55

1006.89 < 1024.55