Question

A coach needs to order 32 softballs for the upcoming season. The softballs used for the batting cages cost $4.25 each. The softballs used for indoor practice cost $3.95 each. The coach has $132.40 to spend on softballs. Write and solve the system of equations.

Answer 1

20 batting cages softballs

12 indoor practice softballs

(20, 12)

Explanation:

let "x" be the number of batting cages softballs

let "y" be the number of indoor practice softballs

x + y = 32 Equation for total softballs

4.25x + 3.95y = 132.40 Equation for cost

Rearrange the equation for total softballs. Isolate one variable.

x + y = 32

y = 32 - x Use this equation to replace "y" in equation for cost

4.25x + 3.95y = 132.40 Equation for cost

4.25x + 3.95(32 - x) = 132.40 Distribute 3.95 over the brackets

4.25x + 126.40 - 3.95x = 132.40 Collect like terms on left side

126.40 + 0.3x = 132.40 Like terms were (4.25x - 3.95x = 0.3x)

126.40 - 126.40 + 0.3x = 132.40 - 126.40 Subtract 126.40 on both sides

0.3x = 6

0.3x/0.3 = 6/0.3 Divide both sides by 0.3

x = 20 Number of batting cages balls

Substitute "x" for 20 in any equation. Isolate "y".

x + y = 32

20 + y = 32

20 - 20 + y = 32 - 20 Subtract 20 from both sides

y = 12 Number of indoor practice balls

The solution is when x is 20 and y is 12. As an ordered pair, or coordinate point, the solution is (20, 12).

This means the coach will buy 20 batting cages softballs and 12 indoor practice softballs.