Question

the sporting goods store sold 10 balls, 3 bats, and 2 bases for $99 on Monday. They sold 4 balls, 8 bats, and 2 bases for $78 on Tuesday. On Wednesday they sold 2 balls 3 bats and 1 base for 33.60. What is the cost of each individual item?

Answer 1

• ball: $8.00
• bat: $5.40
• base: $1.40

Explanation:

Given three relations between the costs of balls, bats, and bases, you want to find the cost of each.

• 10 balls + 3 bats + 2 bases = $99
• 4 balls + 8 bats + 2 bases = $78
• 2 balls + 3 bats + 1 base = $33.60

Solution

Solving three linear equations in three unknowns can be accomplished easily by any number of calculators, apps, or spreadsheets. Here, we'll use an ad hoc solution.

Subtracting twice the third equation from the second, we have ...

(4 balls + 8 bats + 2 bases) -(2(2 balls + 3 bats + 1 base) = 78 -2(33.60)

2 bats = 10.80 . . . . . . . simplify

1 bat = 5.40 . . . . . . divide by 2

Subtracting the second equation from the first, we have ...

(10 balls +3 bats +2 bases) -(4 balls +8 bats +2 bases) = (99) -(78)

6 balls -5 bats = 21 . . . . . simplify

6 balls = 21 + 5(5.40) . . . . . add 5 bats and substitute their cost

6 balls = 48 . . . . . . . . simplify

1 ball = 8.00 . . . . . . . divide by 6

Using the last equation, we can find the cost of 1 base.

1 base = 33.60 -2 balls -3 bats = 33.60 -2(8.00) -3(5.40)

1 base = 1.40

The costs are ...

1 ball: $8.00

1 bat: $5.40

1 base: $1.40