SOLUTION: A certain brand of razor blades comes in packages of 6, 12, and 24 blades, costing $2, $3, and $4 per package, respectively. A store sold 12 packages containing a total of 162 razo

Question 82709This question is from textbook
: A certain brand of razor blades comes in packages of 6, 12, and 24 blades, costing $2, $3, and $4 per package, respectively. A store sold 12 packages containing a total of 162 razor blades and took in $35 dollars. How many packages of each type were sold? This question is from textbook

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A certain brand of razor blades comes in packages of 6, 12, and 24 blades, costing $2, $3, and $4 per package, respectively. A store sold 12 packages containing a total of 162 razor blades and took in $35 dollars. How many packages of each type were sold?
:
Let x = no. of 6 blade pkgs
Let y = no. of 12 blade pkgs
Let z = no. of 24 blade pkgs
:
The no. of pkgs equation:
x + y + z = 12
:
The total cost equation:
2x + 3y + 4z = 35
:
The no. of blades equation
6x + 12y + 24z = 162
:
Multiply the 1st equation by 2 and subtract it from eq 2:
2x + 3y + 4z = 35
2x + 2y + 2z = 24
--------------------subtracting eliminates x
0x + 1y + 2z = 11
y + 2z = 11
y = (11 - 2z); we use this for substitution
:
Multiply equation 1 by 6 and subtract it from equation 3
6x + 12y + 24z = 162
6x + 6y + 6z = 72
---------------------subtracting eliminates x again
0x + 6y + 18z = 90
6y + 18z = 90
:
Substitute (11-2z) for y in the above equation, find z
6(11-2z) + 18z = 90
66 - 12z + 18z = 90
6z = 90 - 66
6z = 24
z = 24/6
z = 4 ea 24 blade pkgs
:
y = 11 - 2z
y = 11 - 2(4)
y = 11 - 8
y = 3 ea 12 blade pkgs
:
Let you figure out what x is using the 1st equation:
:
Check solutions in the 3rd equation:
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