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)

Question

Responses

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 −8
weeks they will have the same amount of gas in their tanks.
After negative 8 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 1.6 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.

Answer 1

To find out when Miguel and Christina will have the same amount of gas in their tanks, we can set up equations based on their usage and the maximum capacity of their tanks.

1. Define Variables:

   • Let \( M(t) \) be the amount of gas in Miguel's tank after \( t \) weeks.
   • Let \( C(t) \) be the amount of gas in Christina's tank after \( t \) weeks.

2. Initial Conditions:

   • Assume both start with a full tank:
     • \( M(0) = 20 \) gallons
     • \( C(0) = 16 \) gallons

3. Gas Usage:

   • Miguel uses 1.5 gallons per week: \[ M(t) = 20 - 1.5t \]
   • Christina uses 1 gallon per week: \[ C(t) = 16 - 1t \]

4. Set the two equations equal: \[ 20 - 1.5t = 16 - 1t \]

5. Solve for \( t \):

   • Rearranging the equation: \[ 20 - 16 = 1.5t - 1t \] \[ 4 = 0.5t \] \[ t = \frac{4}{0.5} = 8 \]

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

The correct response is:

• After 8 weeks they will have the same amount of gas in their tanks.