A faucet is used to add water to a large bottl that already contained some water. after 25 ounces of water. after it has been filling for 11 seconds, the gauge indicates the bottle contains

General
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a faucet is used to add water to a large bottl that already contained some water. after 25 ounces of water. after it has been filling for 11 seconds, the gauge indicates the bottle contains 60 ounces of water. let y be the amount of water in the bottle x t was turned on write a linear equation that models the amount of water in the bottle in terms of x. oa. y–5? 45 1 121 o d. y-5x 49

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LectureNotes said a faucet is used to add water to a large bottle that already contained some water. After 25 ounces of water, after it has been filling for 11 seconds, the gauge indicates the bottle contains 60 ounces of water. Let y be the amount of water in the bottle x was turned on. Write a linear equation that models the amount of water in the bottle in terms of x.

Answer:
To develop a linear equation that models the amount of water in the bottle, we need to identify the relationship between the quantity of water in the bottle and time. From the problem statement, we have the following pieces of information:

  • The bottle already contained some water.
  • After adding 25 ounces of water in 11 seconds, the gauge reads 60 ounces of water.

Steps to solve the problem:

  1. Determine the initial amount of water (before the faucet was turned on):

    • We know that after 25 ounces have been added, the total is 60 ounces.
    • Therefore, the initial amount of water is:
      \text{Initial amount of water} = 60 \, \text{ounces} - 25 \, \text{ounces} = 35 \, \text{ounces}

  2. Determine the rate of water flow (ounces per second):

    • The faucet adds 25 ounces of water in 11 seconds.
    • The rate of water flow is:
      \text{Rate} = \frac{25 \, \text{ounces}}{11 \, \text{seconds}} \approx 2.27 \, \text{ounces/second}

  3. Formulate the linear equation:

    • Let ( y ) be the total amount of water in the bottle (in ounces) and ( x ) be the time in seconds.

    • The relationship follows a linear form:

      y = \text{Initial amount of water} + (\text{Rate of flow} \times x)

    • Plugging in the values:

      y = 35 + \left(\frac{25}{11} \times x\right)

    • Simplified, the linear equation becomes:

      y = 35 + \frac{25}{11}x

Final Answer:
The linear equation that models the amount of water in the bottle in terms of ( x ) (time in seconds) is:

y = 35 + \frac{25}{11}x