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

Answer:

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

Step-by-step 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):

$y=12-4x\\\\y=12-4\times 2\\\\y=12-8\\\\y=4.$

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.