What is the price each for a donut, cookie and scone?

Question

Eight donuts, twelve cookies, and five scones costs $17.95.  Seven donuts, six cookies, and nine scones costs $17.40. Twelve donuts, eighteen cookies, and six scones costs $25.50.  What is the price each for a donut, cookie and scone?

Answer 1

Hello Shawn:

 

Let the prices be d for each donut, c for each cookie and s for each scone.

 

You find d, c and s by solving the equations:

 

 8d + 12c + 5s = 17.95

 7d +   6c + 9s = 17.40

12d + 18c + 6s = 25.50

 

There are many (tedious) ways of solving these equations, by elimination, by Cramer's Rule, by finding the inverse of the matrix of coeficients, and so on.  I will take the HIGH-TECH way out.  Use the website:

 

http://symbolab.com/solver/system-of-equations-calculator

 

Click on the left on System of Equations (NEW) Linear,  and enter the equations as above, no spaces,  separated by commas.  Hit GO (in RED).

You get d = 19/20 = 95 cents, c = 3/5 = 60 cents, s = 3/4 = 75 cents.

 

You do the back check, please.

 

Dr. G.

 

 

 

 

 

 

Answer 2

8x+12y+5z = 1795

7x+6y+9z = 1740

12x+18y+6z = 2550

 

(3/2)[(8x+12y+5z = 1795]

12x+18y+(15/2)z = (3/2)1795

12x+18y+6z = 2550

 

(3/2)z = (3/2)1795 - 2550

z = 95 cents for a scone

 

14x+12y+18z = 3480

8x+12y+5z = 1795

 

6x+13z = 1685

6x+1235 = 1685

6x = 450

x = 75 cents for a donut

Then y = 60 cents for a cookie