Abby and Anita receive water service from two different companies. Anita’s water service costs 30 cents per gallon per month and has a service charge of $25 per month. Abby’s water service costs 10 cents per gallon per month and has a service charge of $35 per month. Let x represent the number of gallons of water per month and y represent the monthly cost. Write the equations that make up the system of equations for this scenario.

Question

Anita’s water bill can be modeled with the equation y=

Abby’s water bill can be modeled with the equation y=

Answer 1

To model the monthly water costs for both Anita and Abby, we can use the following equations:

For Anita:

• The cost of water is 30 cents per gallon, which can be represented as \(0.30x\).
• The service charge is $25 per month.
• Therefore, Anita's total monthly cost, \(y\), can be represented by the equation:

\[ y = 0.30x + 25 \]

For Abby:

• The cost of water is 10 cents per gallon, which can be represented as \(0.10x\).
• The service charge is $35 per month.
• Therefore, Abby's total monthly cost, \(y\), can be represented by the equation:

\[ y = 0.10x + 35 \]

In summary, the system of equations is:

• Anita's water bill: \(y = 0.30x + 25\)
• Abby's water bill: \(y = 0.10x + 35\)