Question 1125748
let x = the number of grams of fiber in a blueberry muffin.
let y = the number of grams of fiber in a banana.
let z= the number of grams of fiber in a serving of cereal.


your equations become:


2x + y + z = 15
x + 2y + z = 17.5
2x + 0y + z = 10


these 3 equations need to be solved simultaneously.


take the first 2 equations and solve for x and y by eliminating z.


you get:


2x + y + z = 15
x + 2y + z = 17.5


subtract the second equation form the first to get x - y = -2.5


take the second and third equatioon and solve for x and y by eliminating z.


2x + y + z = 15
2x + 0y + z = 10


subtract the second equation from the first to get y = 5.


go back to the equation of x - y = -2.5 and replace y with 5 to get:


x - 5 = -2.5
add 5 to both sides of this equation to get x = 2.5


you now have x = 2.5 and y = 5.


go back to the first original equation of 2x + y + z = 15 and replace x with 2.5 and y with 5 to get 5 + 5 + z = 15 which results in z = 5.


your values are:


x = 2.5
y = 5
z = 5


evaluate all 3 original equations to see that they are true when you use these values for x,y,z.


the 3 original equations are:


2x + y + z = 15 which becomes 2*2.5 + 5 + 5 = 15 which becomes 15 = 15.
x + 2y + z = 17.5 which becomes 2.5 + 10 + 5 = 17.5 which becomes 17.5 = 17.5.
2x + 0y + z = 10 which becomes 2*2.5 + 5 = 10 which becomes 10 = 10.


all 3 equations are true, therefore the solution is good.


the solution is:


there are 2.5 grams of fiber in a blueberry muffin.
there are 5 grams of fiber in a banana.
there are 5 grams of fiber in a serving of cereal.