Question

A sporting goods store sells right-handed and left-handed baseball gloves. In one month, 12 gloves were sold for a total revenue of $561. Right-handed gloves cost $45 and left-handed gloves cost $52. How much of each type of gloves did they sell

Answer 1

Answer:

$9$ right-handed gloves and $3$ left-handed gloves were sold.

Step-by-step explanation:

Given:  In one month, $12$ gloves were sold for a total revenue of $\ 561$.

            right-handed gloves cost $\ 45$ and left-handed gloves cost $\ 52$.

To find: How much of each type of gloves did they sell?

Solution: Let they sell $x$  right-handed gloves, and $y$ left-handed gloves.

Now, cost of each right-handed gloves $=\ 45$

cost of each left-handed gloves $=\ 52$

Total revenue $=\ 561$

So, we get

$45x+52y=561\:\:\:...(i)$

Also,  in a month $12$ gloves were sold.

So, we get

$x+y=12\:\:\:...(ii)$

Now, from $(ii)$ we get, $x=12-y$.

Putting $x=12-y$ in equation $(i)$, we get

$45(12-y)+52y=561$

$\implies 540-45y+52y=561$

$\implies7y=561-540$

$\implies7y=21$

$\implies y=\frac{21}{7}$

$\implies y=3$

Now, putting $y=3$ in equation $(ii)$, we get

$x+3=12$

$\implies x=12-3$

$\implies x=9$

Hence, $9$ right-handed gloves and $3$ left-handed gloves were sold.