Question

A gas station attendant is making 1000 gallons of antifreeze that is 48% alcohol. He has some antifreeze that is 40% alcohol and some that is 60% alcohol. How much of each type of antifreeze should he use? (x = amount of 40% alcohol antifreeze and y = amount of 60% alcohol antifreeze)

A) x = 400 gallons, y = 600 gallons
B) x = 500 gallons, y = 500 gallons
C) x = 600 gallons, y = 400 gallons
D) x = 700 gallons, y = 300 gallons

Answer 1

To solve this problem, we can set up a system of equations where x is the amount of 40% alcohol antifreeze and y is the amount of 60% alcohol antifreeze. By solving the system of equations, we find that x = 600 gallons and y = 400 gallons.

Step-by-step explanation:

To solve this problem, we can use a system of equations. Let x be the amount of 40% alcohol antifreeze and y be the amount of 60% alcohol antifreeze.

From the given information, we know that there are a total of 1000 gallons of antifreeze, and it is 48% alcohol.

So, we can set up the following system of equations:

• x + y = 1000 (equation 1)
• 0.4x + 0.6y = 0.48(1000) (equation 2)

We can solve this system of equations using substitution or elimination method. Solving equation 1 for x, we get x = 1000 - y. Substituting this into equation 2, we have:

0.4(1000 - y) + 0.6y = 0.48(1000)

400 - 0.4y + 0.6y = 480

0.2y = 80

y = 400

Substituting the value of y into equation 1, we get x = 1000 - 400 = 600.

Therefore, the solution is x = 600 gallons, y = 400 gallons. Hence, the correct answer is C) x = 600 gallons, y = 400 gallons.