Question 993666
x is the amount of coffee at 9 dollars a pound.
y is the amount of coffee at 12 dollars a pound.


you have two equations:


x + y = 40


9x + 12y = 400


solve these equations simultaneously, and you will get:


x = 26.67
y = 12.33


x + y = 40 becomes 26.67 + 13.33 = 40


9x + 12y = 400 becomes 9 * 26.67 + 12 * 13.33 which becomes 240.03 + 159.96 which becomes 299.99.


the difference from 400 is due to rounding.


26.67 is really 26.6666666666666........


13.33 is really 13.333333333333333........


to get this solution, you need to be able to solve the system of equations simultaneously.


here's a reference on how to do that.


<a href = "http://www.regentsprep.org/regents/math/algebra/ae3/indexAE3.htm" target = "_blank">http://www.regentsprep.org/regents/math/algebra/ae3/indexAE3.htm</a>


i'll use elimination method.


your two equations are:


x + y = 40
9x + 12y = 400


multiply both sides of the first equation by 9 to get:


9x + 9y = 360
9x + 12y = 400


subtract the first equation from the second equation to get:


3y = 40


divide both sides of this equation by 3 to get:


y = 13.33.....
this rounds to 13.33

use that value of y to solve for x in either equation to get:


x = 26.66.....
this rounds to 26.67