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)
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.
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.
To determine when Miguel and Christina will have the same amount of gas in their tanks, we can set up an equation. Miguel's car uses 1.5 gallons per week, so after x weeks, Miguel's car will have 20 - 1.5x gallons of gas. Similarly, Christina's car uses 1 gallon per week, so after x weeks, Christina's car will have 16 - 1x gallons of gas.
Setting the two equations equal to each other:
20 - 1.5x = 16 - x
Simplifying the equation:
-0.5x = -4
Dividing both sides by -0.5:
x = 8
Therefore, after 8 weeks, Miguel and Christina will have the same amount of gas in their tanks.
So the correct answer is:
• After 8 weeks they will have the same amount of gas in their tanks.
To find out when Miguel and Christina will have the same amount of gas in their tanks, we can set up an equation based on their gas usage over time.
Let's assume x represents the number of weeks passed. Miguel uses 1.5 gallons of gas per week, so the amount of gas in his tank after x weeks would be: 1.5x gallons.
Similarly, Christina uses 1 gallon of gas per week, so the amount of gas in her tank after x weeks would be: 1x gallons.
To find when they have the same amount of gas, we need to set up an equation and solve for x. The equation would be:
1.5x = 1x
Now, let's solve for x:
1.5x - 1x = 0.5x
0.5x = 0
x = 0 / 0.5
x = 0
From the equation, we can see that the amount of gas in their tanks will be equal at the start, which is 0 weeks. Therefore, the correct answer is: After 0 weeks they will have the same amount of gas in their tanks.
It's important to note that this answer assumes the tanks are initially empty and does not account for any previous gas consumption before the start of the observation period.