A pencil, eraser and notebook cost a total of S1.00. If a pencil costs more than 2 erasers, 8 erasers cost more than 3 notebooks, and 5 notebooks cost more than 6 pencils, find the cost of a pencil.
+130116 Let the cost ot a pencil be x
Let the cost of a notebook be y
Let the cost of an eraser be z
So
x + y + z = 1.00 ⇒ z = 100 - x - y
x > 2z ⇒ x > 2 (100 -x - y) ⇒ x > 200 - 2x - 2y ⇒ 2y > 200 - 3x (1)
8z > 3y ⇒ 8(100 - x - y) > 3y ⇒ 800 - 8x - 8y > 3y ⇒ 800 - 8x > 11y (2)
5y > 6x (3)
Here is the graph of (1), (2) and (3) :
https://www.desmos.com/calculator/dfd3tgokb7
The integer solutions occur inside the triangle formed by the three inequalites (feasible region)
One is when x = 37, y = 45 ( and z = 18 )
Proof
37 > 2(18) ⇒ 37 > 36
8(18) > 3(45) ⇒ 144 > 135
5(45) > 6(37) ⇒ 225 > 222
So..with this solution......the cost of a pencil = 37 cents
