Final answer:
To create 100 gallons of 92% octane plus gasoline from 90% and 95% octane tanks, we can use a system of equations representing total volume and octane percentage. Upon solving the equations, 60 gallons from the 90% tank and 40 gallons from the 95% tank is the correct mix.
Option B is the correct choice: 60 gallons from the 90% octane tank and 40 gallons from the 95% octane tank.
Step-by-step explanation:
Jayden needs to determine how many gallons from each tank (90% and 95% octane) to use in order to make 100 gallons of 92% octane plus gasoline. Let's use x to represent the amount of gasoline taken from the 90% octane tank and y to represent the amount of gasoline taken from the 95% octane tank. Since he needs a total of 100 gallons, the first equation is:
x + y = 100
For the octane percentage, we use the respective percentages of the two gasoline types and set the equation to equal 92% of 100 gallons, which is the desired octane percentage of the final mixture. The second equation is:
0.90x + 0.95y = 0.92(100)
By solving this system of equations, we can determine the correct amounts of each type of gasoline needed. Using these equations, we identify the correct option from the given choices:
- 55 gallons from the 90% tank, 45 gallons from the 95% tank (Option A)
- 60 gallons from the 90% tank, 40 gallons from the 95% tank (Option B)
- 50 gallons from the 90% tank, 50 gallons from the 95% tank (Option C)
- 65 gallons from the 90% tank, 35 gallons from the 95% tank (Option D)
After solving these equations, we find that Option B is the correct choice: 60 gallons from the 90% octane tank and 40 gallons from the 95% octane tank.