Find the cost of a soccer ball and the cost of a soccer ball bag

Question

A sports equipment is having a sale on soccer balls. A soccer coach purchases 10 balls and 2 ball bags for $155. Another soccer coach purchases 12 soccer balls and 3 soccer ball bags for $189. Find the cost of a soccer ball and the cost of a soccer ball bag.

Answer 1

let x = cost of soccer balls

let y = cost of ball bags

 

10x + 2y = 155    {eqn 1}

12x + 3y = 189    {eqn 2}

 

multiply equation 1 by 3

multiply equation 2 by -2

add equations to eliminate the y variable

solve for x

 

 30x + 6y = 465

-24x - 6y = -378

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6x =  87

 

x = 87/6 = $14.50 per soccer ball

 

Plugging that back into equation 1, solve for y

 

10(14.5) + 2y = 155

145 + 2y = 155

2y = 10

y = $5.00 per ball bag