Question

Mrs Leon bought 6 rolls of toilet paper and 5 bottles of hand sanitizer for $32. Ms Ramirez bought 4 rolls of toilet paper and 1 bottle of hand sanitizer for $12. If the store has one price for toilet paper and one price for hand sanitizers what is the cost for each item sold?

Answer 1

The cost of a roll of toilet paper is $2 and the cost of a bottle of hand sanitizer is $4.

Explanation:

Given:

Mrs Leon bought 6 rolls of toilet paper and 5 bottles of hand sanitizer for $32.

Ms Ramirez bought 4 rolls of toilet paper and 1 bottle of hand sanitizer for $12.

Now, to find the cost for each item sold.

Let the cost of a roll of toilet paper be
`x.`

And the cost of a bottle of hand sanitizer be
`y.`

So, the cost of 4 rolls of toilet paper and 1 bottle of hand sanitizer:

`4x+y=12\\\\y=12-4x\ \ \ \ .....(1)`

Now, the cost of 6 rolls of toilet paper and 5 bottles of hand sanitizer:

`6x+5y=32`

Substituting the value of
`y` from equation (1):

`6x+5(12-4x)=32`

`6x+60-20x=32`

`60-14x=32`

Subtracting both sides by 60 we get:

`-14x=-28`

Dividing both sides by -14 we get:

`x=2.`

The cost of a roll of toilet paper = $2.

Now, substituting the value of
`x` in equation (1):

`y=12-4x\\\\y=12-4* 2\\\\y=12-8\\\\y=4.`

The cost of a bottle of hand sanitizer = $4.

Therefore, the cost of a roll of toilet paper is $2 and the cost of a bottle of hand sanitizer is $4.