Solving a percent mixture problem using a system of linear...
A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. The premiurin antireeze solution contains $85 \%$ pure antifreeze. The company wants to obtain 170 gallons of a mixture that contains $80 \%$ pure antifreeze. How many gailons of water and how many gallons of the premium antifreeze solution must be mixed?
Note that the ALEKS graphing calculator can be used to make computations easier.
Water:
Đgallons
Premium antifreeze:
gallons

Step 1 ：Let's denote the volume of water to be added as \(W\) (in gallons), and the volume of premium antifreeze solution to be added as \(P\) (in gallons).

Step 2 ：From the problem, we know that the total volume of the mixture should be 170 gallons, so we have the equation \(W + P = 170\).

Step 3 ：We also know that the mixture should be 80% pure antifreeze. Since water doesn't contain any antifreeze and the premium solution is 85% antifreeze, we have the equation \(0*W + 0.85*P = 0.8*170\).

Step 4 ：We can solve this system of equations to find the values of \(W\) and \(P\).

Step 5 ：The solution to the system of equations is \(P = 160\) and \(W = 10\).

Step 6 ：This means that to obtain 170 gallons of a mixture that contains 80% pure antifreeze, the company must mix 10 gallons of water with 160 gallons of the premium antifreeze solution.

Step 7 ：Final Answer: The company must mix \(\boxed{10}\) gallons of water with \(\boxed{160}\) gallons of the premium antifreeze solution.