Respuesta :
Given:
The first brand is 30% anti-freeze
The second brand is 70% anti-freeze.
We want to make a 60 gallons mixture that has 40% anti-freeze.
Solution
Let the gallons of the first brand be x
Hence the gallons of the second brand would be:
[tex]=60\text{ - x}[/tex]The gallons of the first brand that would be pure anti-freeze:
[tex]\begin{gathered} =\text{ }\frac{30}{100}\text{ }\times\text{ x} \\ =\text{ 0.3x} \end{gathered}[/tex]The gallons of the second brand that would be pure anti-freeze:
[tex]\begin{gathered} =\text{ }\frac{70}{100}\text{ }\times\text{ (60-x)} \\ =\text{ 0.7(60-x)} \end{gathered}[/tex]The gallons of the mixture that would be pure anti-freeze:
[tex]\begin{gathered} =\text{ }\frac{40}{100}\text{ }\times\text{ 60} \\ =\text{ 0.4 }\times\text{ 60} \\ =\text{ 24} \end{gathered}[/tex]On mixing, we have the equation:
[tex]0.3x\text{ + 0.7(60-x) = 24}[/tex]When we solve for x, we have:
[tex]\begin{gathered} 0.3x\text{ + 42 -0.7x = 24} \\ \text{Collect like terms} \\ 0.3x\text{ - 0.7x = 24 -42} \\ -0.4x\text{ = -18} \\ \text{Divide both sides by -0.4} \\ \frac{-0.4x}{-0.4}\text{ =}\frac{-18}{-0.4} \\ x\text{ = 45} \end{gathered}[/tex]Hence, the gallons of the first brand required to obtain a mixture of 40% anti-freeze is 45 gallons.
The gallons of the second brand required would be:
[tex]\begin{gathered} =60\text{ - 45} \\ =\text{ 15 gallons} \end{gathered}[/tex]Answer:
First brand = 45 gallons
Second brand = 15 gallons
