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

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

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=(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.