13. Part A:
At a clothing store, Ted bought 4 shirts and 2 ties for a total price of [tex]$95. At the same store, Stephen bought 3 shirts and 3 ties for a total price of $[/tex]84. Each shirt was the same price, and each tie was the same price. Which system of equations can be used to find [tex]\( s \)[/tex], the cost of each shirt in dollars, and [tex]\( t \)[/tex], the cost of each tie in dollars?

A. [tex]\( 6(s + t) = 95 \)[/tex]
[tex]\( 3(s + t) = 84 \)[/tex]

B. [tex]\( 4s + 2t = 95 \)[/tex]
[tex]\( 3s + 3t = 84 \)[/tex]

C. [tex]\( 7s + 5t = 179 \)[/tex]
[tex]\( s + t = 12 \)[/tex]

D. [tex]\( 7s + 5t = 179 \)[/tex]
[tex]\( 7s + 5t = 12(s + t) \)[/tex]

Part B:
Linda bought 1 shirt and 2 ties at the same store. What is the total price, in dollars and cents, of Linda's purchase?

[tex]\(\square\)[/tex]



Answer :

Let's break down the problem step by step.

Part A: Formulating the system of equations

We know from the problem that:
- Ted bought 4 shirts and 2 ties for a total of \[tex]$95. - Stephen bought 3 shirts and 3 ties for a total of \$[/tex]84.

We need to use these statements to formulate a system of equations.
Let's denote:
- [tex]\( s \)[/tex] as the cost of one shirt in dollars.
- [tex]\( t \)[/tex] as the cost of one tie in dollars.

From Ted's purchase, we have the equation:
[tex]\[ 4s + 2t = 95 \][/tex]

From Stephen's purchase, we have the equation:
[tex]\[ 3s + 3t = 84 \][/tex]

Looking at the given options, we find that Option B matches our equations:
[tex]\[ 4s + 2t = 95 \][/tex]
[tex]\[ 3s + 3t = 84 \][/tex]

Hence, the correct answer for Part A is:
B. [tex]\( 4s + 2t = 95 \)[/tex], [tex]\( 3s + 3t = 84 \)[/tex]

Now we'll solve this system of equations to find the values of [tex]\( s \)[/tex] and [tex]\( t \)[/tex].

Part B: Solving the system of equations

Using the system of equations:
[tex]\[ 4s + 2t = 95 \][/tex]
[tex]\[ 3s + 3t = 84 \][/tex]

We solve these equations simultaneously.

From solving these equations, the solutions are:
[tex]\[ s = \frac{39}{2} \][/tex]
[tex]\[ t = \frac{17}{2} \][/tex]

This means the cost of each shirt ([tex]\(s\)[/tex]) is \[tex]$19.50 and the cost of each tie (\(t\)) is \$[/tex]8.50.

Part C: Calculating the total price for Linda's purchase

Linda bought 1 shirt and 2 ties. To find the total price, we calculate:
[tex]\[ \text{Total price} = 1 \times s + 2 \times t \][/tex]

Substituting the values of [tex]\( s \)[/tex] and [tex]\( t \)[/tex]:
[tex]\[ \text{Total price} = 1 \times \frac{39}{2} + 2 \times \frac{17}{2} \][/tex]

This simplifies to:
[tex]\[ \text{Total price} = \frac{39}{2} + \frac{34}{2} = \frac{73}{2} = 36.50 \][/tex]

So, the total price of Linda's purchase is:
[tex]\[ \$ 36.50 \][/tex]

Therefore, the total price, in dollars and cents, of Linda's purchase is \$36.50.