Question

A family orders four chickens and two hamburgers and pays 28 dollars.

Another family buys 3 chickens and 3 hamburgers and pays 36$

Let x = chicken and y = hamburger.

How much is each chicken and each hamburger

a
Burger costs 2$ and chicken costs 10$

b
Chicken costs 2$

Burger costs 10$

c
Chicken costs 6.50$ and burger costs 4.75$

Answer 1

Let's set up the equations based on the information given:

1. From the first family's order:
\[
4x + 2y = 28
\]

2. From the second family's order:
\[
3x + 3y = 36
\]

Now we will simplify these equations:

1. Divide the first equation by 2:
\[
2x + y = 14 \quad \text{(Equation 1)}
\]

2. Divide the second equation by 3:
\[
x + y = 12 \quad \text{(Equation 2)}
\]

Next, we can solve these two equations. We can express \(y\) from Equation 2:

From Equation 2:
\[
y = 12 - x
\]

Now, substitute \(y\) in Equation 1:
\[
2x + (12 - x) = 14
\]
\[
2x + 12 - x = 14
\]
\[
x + 12 = 14
\]
\[
x = 2
\]

Now substitute \(x = 2\) back into Equation 2 to solve for \(y\):
\[
2 + y = 12
\]
\[
y = 12 - 2
\]
\[
y = 10
\]

Thus, we have:
- \(x = 2\) (the cost of a chicken) and
- \(y = 10\) (the cost of a hamburger).

So the correct option is:
**b**
- Chicken costs **2$**.
- Burger costs **10$**.