Playground Equipment Prices
SETTING UP SYSTEM OF EQUATIONS FOR A MATRIX?
The director of a public playground is ordering a supply of baseball equipment. He wishes to
have two gloves for every ball and one bat for every three gloves. The unit prices for gloves,
bats, and balls are $4.00, $3.00, and $0.50, respectively. The director has a budget of $157.50.
What equipment should be ordered?
Set up the system of equations (don’t forget to define your variables), put it in matrix format, and
solve using row operations to get to the reduced row-echelon form.
i’m fine with the matrix part, i just need the equations to work with
any help is greatly appreciated
Let x = # of gloves
Let y = # of balls
Let z = # of bats
He wishes to have two gloves for every ball and one bat for every three gloves. =>
2x = 1y => 2x = y
1z = 3x => z = 3x => 2z = 2*3x = 3*2x = 3y=>
3y – 2z = 0
The unit prices for gloves, bats, and balls are $4.00, $3.00, and $0.50, respectively. The director has a budget of $157.50.
157.5 =
(4)x + (.5y) + 3z =
2*2x + .5y + 3z =
2y + .5y + 3z =
2.5y + 3z =>
2.5y + 3z = 157.5 => 5y + 6z = 315
So our two equations are
3y – 2z = 0
5y + 6z = 315,
When you are done, you need to go back and solve for x using, 2x =y, or you can convert the above to a 3×3 system as follows:
2x – y + 0z = 0
0x + 3y – 2z = 0
0x + 5y + 6z = 315
Mike Burnside: Comprehensive Bootcamp using playground equipment
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