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You want to make a mixture of peanuts and cashews to sell. Peanuts
cost \$3 per pound and cashews cost \$9 per pound.
Let’s see what happens to the cost of a 10-pound mixture if you mix different amounts of
peanuts and cashews.
We want to make a 10-pound mixture of peanuts and cashews. This means that if we use
$x$ pounds of peanuts, we will have to use $10-x$ pounds of cashews.
Cashews cost \$9 per pound, so the total cost (in dollars) of the cashews will be $9(10-x)$.
The total cost of the mixture can be found by adding the cost of the cashews to the cost of the
peanuts. That is, $\text"Total Cost" = 3x + 9(10-x)$.
If $y$ is the cost per pound of the mixture, then we have:
You want to combine a 20% methanol solution with a 60% methanol solution
to make 10 liters of a mixture.
Another way to look at the 52% solution part of
as a system of equations. We want to know how much of each of the 20% and 60% solutions should
be mixed to get 10 liters of a 52% solution. This time, let $x$
be the number of liters of the 20% solution and $y$
be the number of liters of the 60% solution. Then the system of linear equations is:
The first equation in this system represents the total amount of methanol
in the mixture, while the second equation represents the total amount of
In alc2, you found out how much of the 20% and 60%
solutions need to be mixed to make 10 liters of a 52% solution. Now let’s mix solutions with
different concentrations and see how much of each we need to make 10 liters of a 52%
Call the concentration of the first solution $a$ and the concentration of the second solution
$b$. Using $a$ and $b$, our system becomes:
Using the sliders, complete the table below. $x$ is the amount of
the first solution and $y$ is the amount of the second solution.
Remember to use the vertical bar in the grid to the left to find the point of intersection of
the two lines.