Miguel’s car has a 20-gallon capacity, and Christina’s car has a 16-gallon capacity. Miguel uses 1.5 gallons of gas per week, and Christina uses 1 gallon of gas per week. When will Miguel and Christina have the same amount of gas in their tanks?(1 point) Responses After 1.6 weeks they will have the same amount of gas in their tanks. After 1.6 weeks they will have the same amount of gas in their tanks. After 8 weeks they will have the same amount of gas in their tanks. After 8 weeks they will have the same amount of gas in their tanks. After 18 week they will have the same amount of gas in their tanks. After Start Fraction 1 over 8 End Fraction week they will have the same amount of gas in their tanks. After −8 weeks they will have the same amount of gas in their tanks.

Answer 1

To find out when Miguel and Christina will have the same amount of gas in their tanks, we need to set up a comparison of how much gas each has after some weeks.

Let \( t \) represent the number of weeks.

1. Miguel's gas usage:

   • Miguel starts with a full tank of 20 gallons and uses 1.5 gallons per week.
   • So, after \( t \) weeks, the amount of gas Miguel has is: \[ M(t) = 20 - 1.5t \]

2. Christina's gas usage:

   • Christina starts with a full tank of 16 gallons and uses 1 gallon per week.
   • So, after \( t \) weeks, the amount of gas Christina has is: \[ C(t) = 16 - t \]

Now we set the two equations equal to each other in order to find the point at which they have the same amount of gas: \[ 20 - 1.5t = 16 - t \]

Now, let’s solve for \( t \):

1. Rearranging: \[ 20 - 16 = -t + 1.5t \] \[ 4 = 0.5t \]

2. Dividing both sides by 0.5: \[ t = \frac{4}{0.5} = 8 \]

Thus, Miguel and Christina will have the same amount of gas in their tanks after 8 weeks.

Therefore, the correct response is: After 8 weeks they will have the same amount of gas in their tanks.