Question

In a certain clothing store, 6 shirts and 3 ties cost $79.50, and 3 shirts and 2 ties cost $41. Determine the cost of each tie.

A. $2.50
B. $3.50
C.$4.50

Answer 1

Answer 2

A. $2.50

Explanation:

Let s be the cost of shirt and t be the cost of each tie.

We have been given that in a certain clothing store, 6 shirts and 3 ties cost $79.50. We can represent this information in an equation as:

`6s+3t=79.50...(1)`

We are also told that 3 shirts and 2 ties cost $41. We can represent this information in an equation as:

`3s+2t=41...(2)`

Now, we will use substitution method of solving system of equations. From equation (1) we will get,

`s=(79.50-3t)/(6)`

Substituting this value in equation (2):

`3((79.50-3t)/(6))+2t=41`

`(79.50-3t)/(2)+2t=41`

`(79.50-3t)/(2)+(2*2t)/(2)=41`

`(79.50-3t+4t)/(2)=41`

Now, we will multiply both sides of our equation by 2.

`(79.50+t)/(2)*2=41*2`

`79.50+t=82`

Subtracting 79.50 from both sides we will get,

`79.50-79.50+t=82-79.50`

`t=2.50`

Therefore, the cost of each tie is $2.50 and option A is the correct choice.