Answered

From science to arts, IDNLearn.com has the answers to all your questions. Our platform provides detailed and accurate responses from experts, helping you navigate any topic with confidence.

The county water department charges a service fee of [tex]$10.15 plus $[/tex]0.005 for each gallon of water used. The number of gallons of water, [tex]\( x \)[/tex], used by customers whose monthly charges range from [tex]$35 to $[/tex]55 is represented by the inequality:

[tex]\[ 35 \leq 10.15 + 0.005x \leq 55 \][/tex]

Which statement best describes the gallons of water used by the customers with charges represented by the inequality?

A. These customers use at least 4,970 gallons but no more than 8,970 gallons of water per month.
B. These customers use more than 6,990 gallons but less than 10,990 gallons of water per month.
C. These customers use more than 4,970 gallons but less than 8,970 gallons of water per month.
D. These customers use at least 6,990 gallons but no more than 10,990 gallons of water per month.

Sagot :

GinnyAnsweridn
To determine the range of gallons of water used by customers whose monthly charges range from [tex]$35 to $[/tex]55, we need to solve the inequality:
[tex]\[ 35 \leq 10.15 + 0.005x \leq 55 \][/tex]

First, let's isolate [tex]\( x \)[/tex] in the inequality by solving for [tex]\( x \)[/tex] in both the lower and upper bounds.

### Solving for the lower bound:
[tex]\[ 35 \leq 10.15 + 0.005x \][/tex]

1. Subtract 10.15 from both sides:
[tex]\[ 35 - 10.15 \leq 0.005x \][/tex]
[tex]\[ 24.85 \leq 0.005x \][/tex]

2. Divide both sides by 0.005:
[tex]\[ \frac{24.85}{0.005} \leq x \][/tex]
[tex]\[ 4970 \leq x \][/tex]

### Solving for the upper bound:
[tex]\[ 10.15 + 0.005x \leq 55 \][/tex]

1. Subtract 10.15 from both sides:
[tex]\[ 0.005x \leq 55 - 10.15 \][/tex]
[tex]\[ 0.005x \leq 44.85 \][/tex]

2. Divide both sides by 0.005:
[tex]\[ x \leq \frac{44.85}{0.005} \][/tex]
[tex]\[ x \leq 8970 \][/tex]

Combining both results, we get:
[tex]\[ 4970 \leq x \leq 8970 \][/tex]

Thus, the customers use at least 4,970 gallons but no more than 8,970 gallons of water per month.

The best statement that describes this is:
A. These customers use at least 4,970 gallons but no more than 8,970 gallons of water per month.
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Thank you for trusting IDNLearn.com. We’re dedicated to providing accurate answers, so visit us again for more solutions.