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.

Question

legenddarkseidlegend legenddarkseidlegend

16-06-2024
Mathematics

Answered

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.

Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-06-16T03:19:13-04:00

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.