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