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

O After 1
§ 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.
• 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.

Answer 1

To find out when Miguel and Christina will have the same amount of gas in their tanks, we can set up an equation.

Let x be the number of weeks it takes for them to have the same amount of gas.

For Miguel, the amount of gas used in x weeks is 1.5 * x.
For Christina, the amount of gas used in x weeks is 1 * x.

Since both cars start with a full tank of gas, the total gas in their tanks must equal their respective capacities:

Miguel's gas in x weeks = 20 - 1.5 * x
Christina's gas in x weeks = 16 - 1 * x

Setting these two expressions equal to each other, we get:

20 - 1.5 * x = 16 - 1 * x

Simplifying the equation:

4 = 0.5 * x

Dividing both sides by 0.5:

8 = x

Therefore, 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.