A sporting goods store sells right handed and left handed baseball gloves. In 1 one month, 12 gloves were sold for a goal of $561. Right handed gloved cost $45 each and left handed gloved cost $52 each How many of each type of glove were sold?

Answer 1

Let's define the variables:

• Let \( x \) be the number of right-handed gloves sold.
• Let \( y \) be the number of left-handed gloves sold.

From the information given, we can set up the following two equations:

1. The total number of gloves sold is 12: \[ x + y = 12 \]

2. The total revenue from the gloves sold is $561: \[ 45x + 52y = 561 \]

Now we will solve this system of equations.

Step 1: Solve for one variable in terms of the other using the first equation.

From the first equation, we can express \( y \) in terms of \( x \): \[ y = 12 - x \]

Step 2: Substitute this expression into the second equation.

Substituting \( y \) into the second equation gives: \[ 45x + 52(12 - x) = 561 \]

Step 3: Simplify and solve for \( x \).

Distributing the 52: \[ 45x + 624 - 52x = 561 \]

Combine like terms: \[ -7x + 624 = 561 \]

Isolate \( x \): \[ -7x = 561 - 624 \] \[ -7x = -63 \] \[ x = 9 \]

Step 4: Solve for \( y \) using the value of \( x \).

Substituting \( x \) back into the equation for \( y \): \[ y = 12 - 9 = 3 \]

Conclusion: The store sold:

• 9 right-handed gloves
• 3 left-handed gloves

To verify:

• Total number of gloves: \( 9 + 3 = 12 \) (correct)
• Total revenue: \( 45(9) + 52(3) = 405 + 156 = 561 \) (correct)

Thus, the solution is:

• Right-handed gloves sold: 9
• Left-handed gloves sold: 3