Q21. - Algebra 1

Question

ABC Sporting Goods Company produces baseball gloves. Their fixed monthly production cost is $\mathrm{\backslash (}8000$ with a per glove cost of $\mathrm{\backslash )}5$ XYZ Sporting Goods Company also produces baseball gloves. Their fixed monthly production cost is $\mathrm{\backslash (}10,000$ with a per glove cost of $\mathrm{\backslash )}3$. Find the value of $x$, the number of gloves produced monthly, so that the total monthly production cost is the same for both companies.

Step-by-Step Solution

Answer

The number of gloves produced monthly $1000$.

Step 1. Given information.

ABC company has fixed monthly production cost is $\mathrm{\$}8000$ with a per glove cost of $\mathrm{\$}5$.

XYZ company has fixed monthly production cost is $\mathrm{\$}10,000$ with a per glove cost of $\mathrm{\$}3$.

The number of gloves produced monthly is $=x$.

Step 2. To find the expression of the problem.

From the given conditions:

The monthly production of the ABC company is $=8000+5x$.

The monthly production of the XYZ company is $=10000+3x$

From the question,

Both the company has the same monthly production.

So, $8000+5x=10000+3x$

Therefore, the expression of the question is 

Step 3. To find the value of x.

To solve the above equation:

$$\begin{gathered} 8000+5x=10000+3x \\ 5x-3x=10000-8000 \\ 2x=2000 \\ x=1000 \end{gathered}$$

Hence, the number of gloves produced monthly $1000$.