Question

You are getting ready to move and have asked some friends to help. For lunch, you buy the following Pub subs at Publix for $30: six chicken tender Pub subs and six deli ultimate Pub subs. Later at night, everyone is hungry again and you buy four chicken tender Pub subs and eight deli ultimate Pub subs for $30.60. What is the price of each Pub sub?

Answer 1

Let's denote the price of the chicken tender Pub sub as $x$ and the price of the deli ultimate Pub sub as $y$.

From the information provided, we can set up the following equations based on the purchases:

1. For the first lunch purchase: $$6x+6y=30$$ We can simplify this equation by dividing everything by 6: $$x+y=5\text{(Equation 1)}$$

2. For the later night purchase: $$4x+8y=30.60$$ We can simplify this equation by dividing everything by 4: $$x+2y=7.65\text{(Equation 2)}$$

Now we have a system of equations: \[ \begin{align*}

1. & \quad x + y = 5 \
2. & \quad x + 2y = 7.65 \end{align*} \]

Next, we'll solve these equations. We can express $y$ from Equation 1: $$y=5-x$$

Now we can substitute this expression for $y$ into Equation 2: $$x+2(5-x)=7.65$$

Distributing the 2: $$x+10-2x=7.65$$

This simplifies to: $$10-x=7.65$$

Now, solving for $x$: $$-x=7.65-10$$ $$-x=-2.35$$ $$x=2.35$$

Now that we have the price of the chicken tender Pub sub, we can find $y$: $$y=5-x=5-2.35=2.65$$

Thus, the prices of the Pub subs are:

• Chicken tender Pub sub: $\boxed{{\displaystyle 2.35}}$
• Deli ultimate Pub sub: $\boxed{{\displaystyle 2.65}}$