Question

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 −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 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 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 determine when Miguel and Christina will have the same amount of gas in their tanks, we can set up equations based on their gas usage and capacities.

Let:
- \( M \) represent the amount of gas Miguel has after \( t \) weeks.
- \( C \) represent the amount of gas Christina has after \( t \) weeks.

**Miguel's gas:**
- Initial capacity: 20 gallons
- Usage: 1.5 gallons per week
- Amount left after \( t \) weeks:
\[ M = 20 - 1.5t \]

**Christina's gas:**
- Initial capacity: 16 gallons
- Usage: 1 gallon per week
- Amount left after \( t \) weeks:
\[ C = 16 - t \]

**Set the amounts equal to each other:**
\[ 20 - 1.5t = 16 - t \]

**Now solve for \( t \):**
1. Rearranging gives:
\[ 20 - 16 = 1.5t - t \]
2. Simplify:
\[ 4 = 0.5t \]
3. Divide both sides by 0.5:
\[ t = 8 \]

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

The correct answer is:
**After 8 weeks they will have the same amount of gas in their tanks.**