Question

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**