Question

5 hockey pucks and 3 hockey sticks cost $63. 5 hockey pucks and and 1 hockey stick cost $31. How much does one hockey puck cost?

Answer 1

application of two simultaneous equations in algebra...
if we let p = cost of a puck
s = cost of stick
from the first statement, we have\[5p+3s=63~~~~(1)\]from the second statement, \[5p+s=31~~~~(2)\]and manipulating (2), solving for s...\[s=31-5p~~~~(3)\]substitute (3) to (1) and solve for p...\[5p+3(31-5p)=63\]by distributive property...\[5p+93-15p=63\]combine like terms and subtract 93 both sides...\[5p-15p+\bcancel{93}-\bcancel{93}=63-93\]\[-10p=-30\]divide both side by -10...\[p=\frac{-30}{-10}\]\[p=3~dollars~per~hockey~puck\]