I'm given the following data on a problem:
A company wants to produce a beverage AZ which is a mixture of beverage A and Z.
Cost/liter of A = 3.00$
Cost/liter of Z = 2.00$
I'm asked to determine the quatities of A and Z required to make 600 liters of AZ at 2.75$ per liter.
How would I go about finding the exact ratio for the ammount required?
I've tried going with a 50% to 50% ratio but it gets me to 2.5$/liter. I can go trial by error on ratios until I get it right, but something tells me that there is a way to get the exact solution required. If someone could help me get the logic going that would be nice. Thanks in advance.
What percent of $A$ and what percent of $Z$ do you need to create something that costs $\$2.75\text{ per liter}$?
Let $x$ be the percentage of $A$ you use. The cost for $1$ liter would be:
$$x\times\$3.00+(1-x)\times\$2.00$$
Solve for $x$ that makes the cost $\$2.75$.
$$3x+2(1-x)=2.75\\3x+2-2x=2.75\\x=.75$$
$75\%$ of $A$ and $25\%$ of $Z$ gets you a drink that costs $\$2.75\text{ per liter}$.