5 hockey pucks and three hockey sticks costs $23. 5 hockey pucks and 1 hockey stick costs $20. How much does 1 hockey puck cost?
5p + 3s = 23
5p + s = 20
s = 20 - 5p
5p + 3(20-5p) = 23
5p - 60 - 15p = 23
-10p = - 37
p = 3.70
s = 1.50
P=cost of pucks S=cost of sticks
1.5P+3S=23 2.5P+S=20 ___________________ 5P+3S-5P-S=23-20 2S=3 S=3/2 ___________________ 5P+3/2=20 5P=40/2-3/2 P=37/10
∴Pucks cost $3.70 and sticks cost $1.50.
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To find out how much one hockey puck costs, we can use algebraic equations to represent the given information. Let's assume the cost of one hockey puck is 'x' dollars.
According to the first statement, 5 hockey pucks and three hockey sticks cost $23. So, the equation for this statement would be: 5x + 3y = 23, where 'y' represents the cost of one hockey stick.
According to the second statement, 5 hockey pucks and one hockey stick cost $20. So, the equation for this statement would be: 5x + y = 20.
Now, we have a system of equations:
Equation 1: 5x + 3y = 23
Equation 2: 5x + y = 20
We can solve this system of equations to find the value of 'x'. We can subtract Equation 2 from Equation 1 to eliminate 'y':
(5x + 3y) - (5x + y) = 23 - 20
2y = 3
y = 3/2
y = 1.5
Now, substitute the value of 'y' back into Equation 2:
5x + 1.5 = 20
5x = 20 - 1.5
5x = 18.5
x = 18.5/5
x = 3.7
Therefore, the cost of one hockey puck is $3.70.