1. Mixture Problems
In two variables

2. Mixture Problems
Now that we know how to solve equations involving more than one variable, story problems will be much easier!
We will use
x to represent one item in the story and y to represent the other item.

3. Mixture Problems
A coffee shop owner wants to make 50 lbs of a new coffee blend by mixing
beans that sell for $12/lb
with beans that sell for $8/lb.
She will sell for the new blend for $9/lb.
How many pounds of each type of bean should she use?

4. Mixture Problems Let x = the number of pounds of $12/lb beans
Let y = the number of pounds of $8/lb beans
We know that she is making 50 pounds of the new blend so our first equation is x + y = 50

5. Mixture Problems Let x = the number of pounds of $12/lb beans
The value of the $12/lb beans is
$12 times the number of pounds of those beans (x).
Therefore, the value of those beans is 12x

6. Mixture Problems Let y = the number of pounds of $8/lb beans
The value of the $8/lb beans is
$8 times the number of pounds of those beans (y).
Therefore, the value of those beans is 8y.

7. Mixture Problems We know the value of the new blend is
the value of the $12 beans + the value of the $8 beans
or 12x + 8y.
And we know that
50 pounds of beans worth $9/pound is
50(9) or $450.
12x + 8y = 450

8. Now we can put our two equations together:
Mixture Problems
Now we can put our two equations together:
x + y = 50
12x + 8y = 450

9. Mixture Problems
We know how to solve that!

10. Mixture Problems Let’s check it! Our original equations were:
x + y = 50
12x + 8y = 450
= 50 check
12.5(12) (8) = 450
= 450 check

11. are easier when you use two variables!
Mixture Problems
are easier when you use two variables!