Question

A chemical company makes two brands of antifreeze. The first brand is 40% pure antifreeze, and the second brand is 90% pure antifreeze. In order to obtain

140 gallons of a mixture that contains 75% pure antifreere, how many gallons of each brand of antifreeze must be used?

Answer 1

Let $x$ be the number of gallons of the 40% antifreeze and $y$ be the number of gallons of the 90% antifreeze. We know that the total amount of antifreeze is 140 gallons, so $x+y=140$. We also know that the final mixture should have 75% pure antifreeze, so the amount of pure antifreeze in the mixture is 0.75(140) = 105 gallons. We can set up a system of equations to solve for $x$ and $y$:

$$0.4x + 0.9y = 105$$

$$x+y = 140$$

Solving the system of equations, we get $x=60$ and $y=80$. Therefore, the chemical company must use 60 gallons of the 40% antifreeze and 80 gallons of the 90% antifreeze.

Here is a step-by-step solution:

1. Let $x$ be the number of gallons of the 40% antifreeze and $y$ be the number of gallons of the 90% antifreeze.

2. Set up a system of equations to represent the given information:

$$x+y = 140$$

$$0.4x + 0.9y = 105$$

3. Solve the system of equations:

$$x = 60$$

$$y = 80$$

4. Therefore, the chemical company must use 60 gallons of the 40% antifreeze and 80 gallons of the 90% antifreeze.

Explanation: