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.

Answer 1

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Answer 2

Answer:

A. $2.50

Step-by-step 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,

$s=\frac{79.50-3t}{6}$

Substituting this value in equation (2):

$3(\frac{79.50-3t}{6})+2t=41$

$\frac{79.50-3t}{2}+2t=41$

$\frac{79.50-3t}{2}+\frac{2*2t}{2}=41$

$\frac{79.50-3t+4t}{2}=41$

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

$\frac{79.50+t}{2}*2=41*2$

$79.50+t=82$

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.