Question 1186116
let x = number of pounds of indonesian cinnamon.
let y = number of pounds of thai cinnamon.
let x + y = number of pounds of brand M cinnamon.


your equations are:


x + y = 16
19 * x + 11 * y = 17 * (x + y)


simplify the second equation to get:
19 * x + 11 * y = 17 * x + 17 * y
subtract the right side of the equation from both sides of the equation to get:
19 * x - 17 * y + 11 * y - 17 * y = 0
combine like terms to get:
2 * x - 6 * y = 0


your two equations become:


x + y = 16
2 * x - 6 * y = 0


multiply both sides of the first equation by 2 and leave the second equation as is to get:


2x + 2y = 32
2x - 6y = 0


subtract the second equation from the first to get:


8y = 32


solve for y to get:


y = 32/8 = 4


in the first equation, replace y with 4 to get:


x + y = 16 becomes x + 4 = 16
solve for x to get:
x = 16 - 4 = 12


you have:


x = 12
y = 4


first equation of x + y = 16 becomes 12 + 4 = 16 which becomes 16 = 16.


second equation of 19x + 11y = 17(x + y) becomes:


19*12 = 11*4 = 17 * 16 which becomes 272 = 272.


the values of x = 12 and y = 4 appear to be good.


you take 12 pounds of indonesiann cinnamon, which is 19 dollars a pound, and mix it with 4 pounds of thai cinnamon, which is 11 dollars a pound, you will get 16 pounds of brand M cinnamon which costs (19 * 12 + 11 * 4) / 16 = 17 dollars a pound.


your solution is that you used 12 pounds of indonesian cinnamon and 4 pounds of thai cinnamon.