Answer:
The ice cream maker should mix 210 gallons of ice cream with 4% butterfat and 90 gallons of the ice cream with 14% butterfat.
Step-by-step explanation:
We are given the following in the question:
We want the mixture with 7% butterfat.
Amount of mixture = 300 gallons
Amount of butterfat in mixture =
[tex]7\%\times 300\\\\=\dfrac{7}{100}\times 300\\\\= 21[/tex]
Let x gallons of 4% butterfat used in mixture.
Butterfat in x gallons =
[tex]4\%\times x\\\\=\dfrac{4}{100}\times x\\\\= 0.04x[/tex]
Amount of 14% butterfat used in mixture =
[tex](300-x)\text{ gallons}[/tex]
Butterfat in (300-x) gallons =
[tex]14\%\times (300-x)\\\\=\dfrac{14}{100}\times (300-x)\\\\= 0.14(300-x)[/tex]
Thus, we can write the equation:
Butterfat in mixture =
[tex]21 = 0.04x + 0.14(300-x)\\21 = 0.04x + 42 -0.14x\\0.1x = 21\\x = 210\\\Rightarrow 300-x = 90[/tex]
Thus, the ice cream maker should mix 210 gallons of ice cream with 4% butterfat and 90 gallons of the ice cream with 14% butterfat.
