Answer:
right-handed gloves and
left-handed gloves were sold.
Step-by-step explanation:
Given: In one month,
gloves were sold for a total revenue of
.
right-handed gloves cost
and left-handed gloves cost
.
To find: How much of each type of gloves did they sell?
Solution: Let they sell
right-handed gloves, and
left-handed gloves.
Now, cost of each right-handed gloves ![=\$45](https://tex.z-dn.net/?f=%3D%5C%2445)
cost of each left-handed gloves ![=\$52](https://tex.z-dn.net/?f=%3D%5C%2452)
Total revenue ![=\$561](https://tex.z-dn.net/?f=%3D%5C%24561)
So, we get
![45x+52y=561\:\:\:...(i)](https://tex.z-dn.net/?f=45x%2B52y%3D561%5C%3A%5C%3A%5C%3A...%28i%29)
Also, in a month
gloves were sold.
So, we get
![x+y=12\:\:\:...(ii)](https://tex.z-dn.net/?f=x%2By%3D12%5C%3A%5C%3A%5C%3A...%28ii%29)
Now, from
we get,
.
Putting
in equation
, we get
![45(12-y)+52y=561](https://tex.z-dn.net/?f=45%2812-y%29%2B52y%3D561)
![\implies 540-45y+52y=561](https://tex.z-dn.net/?f=%5Cimplies%20540-45y%2B52y%3D561)
![\implies7y=561-540](https://tex.z-dn.net/?f=%5Cimplies7y%3D561-540)
![\implies7y=21](https://tex.z-dn.net/?f=%5Cimplies7y%3D21)
![\implies y=\frac{21}{7}](https://tex.z-dn.net/?f=%5Cimplies%20y%3D%5Cfrac%7B21%7D%7B7%7D)
![\implies y=3](https://tex.z-dn.net/?f=%5Cimplies%20y%3D3)
Now, putting
in equation
, we get
![x+3=12](https://tex.z-dn.net/?f=x%2B3%3D12)
![\implies x=12-3](https://tex.z-dn.net/?f=%5Cimplies%20x%3D12-3)
![\implies x=9](https://tex.z-dn.net/?f=%5Cimplies%20x%3D9)
Hence,
right-handed gloves and
left-handed gloves were sold.