Foodie question

Question

Chery brought 5 burritos, 3 milks, and 15 hash browns for $41. Sam bought 8 burritos,1 milk, and 3 hash browns for $37. Karla bought 3 burrito, 4 milks, 6 hash browns for $26  What is the cost of each ind item?

Answer 1

Let's create 3 different equations, one for each person. We will assign the variable "b" for burritos, "m" for milk, and "h" for hashbrowns:

 

Chery

5b + 3m + 15h = 41

 

Sam

8b + m + 3h = 37

 

Karla

3b + 4m + 6h = 26

 

 

Solve the system of equations by using the elimination method. I am going to multiply Sam's equation times (-3), so that the variable "m" cancels out when adding Chery's and Sam's equations together [8b + m + 3h = 37 turns into -24b - 3m - 9h = -111].

 

5b + 3m + 15h = 41

-24b - 3m - 9h = -111

____________________

-19b + 6h = -70

 

 

Now, I am going to multiply Sam's equation times (-4), so that the variable "m" cancels out when adding Karla's and Sam's equations together [8b + m + 3h = 37 turns into -32b - 4m - 12h = -148].

3b + 4m + 6h = 26
-32b - 4m - 12h = -148
____________________
-29b - 6h = -122

 

 

Now we have two equations, each having the two variables "b" and "h". Since one equation has "+6h" and the other has "-6h", if we add these two equations together, the variable "h" will be cancelled altogether.

 

-19b + 6h = -70

-29b - 6h = -122

_______________

-48b = -192

b = 4

 

Now that we found that b = 4, we can substitute that value into either of the two equations that have "b" and "h", and then we can solve for "h".

 

-19b + 6h = -70

-19(4) + 6h = -70

6h = 6

h = 1

 

Now that we found that b = 4 and h = 1, we can substitute those values into any of the three original equations that have "b" "h" and "m", and then we can solve for "m".

 

8b + m + 3h = 37

8(4) + m + 3(1) = 37

32 + m + 3 = 37

m + 35 = 37

m = 2

 

 

 

The burritos cost $4, the milk cost $2, and the hash browns cost $1.