Question

applying a system of equations to a situation
a deli sells sliced meat and cheese. one customer purchases 4 pounds of meat and 5 pounds of cheese for a total of $30.50. a sandwich shop owner comes in and purchases 11 pounds of meat and 14 pounds of cheese for $84.50.
the system of equations below represents the situation.
4x + 5y = 30.50
11x + 14y = 84.50
the variable x represents the
the variable y represents the
the deli charges $
number of customers
number of slices of meat
cost per pound of meat
total pounds of meat

Explanation:

Step1: Match variable to quantity

In the equation $4x + 5y = 30.50$, 4 is the number of pounds of meat purchased. When multiplied by $x$, it gives the total cost of the meat. So $x$ must be the cost per pound of meat.

Step2: Identify y's meaning

Similarly, 5 is the number of pounds of cheese. When multiplied by $y$, it gives the total cost of the cheese. So $y$ must be the cost per pound of cheese.

Step3: Solve for x and y

First, multiply the first equation by 11:
$$11*(4x + 5y) = 11*30.50$$
$$44x + 55y = 335.5$$
Multiply the second equation by 4:
$$4*(11x + 14y) = 4*84.50$$
$$44x + 56y = 338$$
Subtract the new first equation from the new second equation:
$$(44x + 56y) - (44x + 55y) = 338 - 335.5$$
$$y = 2.5$$
Substitute $y=2.5$ into $4x + 5y = 30.50$:
$$4x + 5*2.5 = 30.50$$
$$4x + 12.5 = 30.50$$
$$4x = 30.50 - 12.5$$
$$4x = 18$$
$$x = 4.5$$

Answer:

The variable $x$ represents the: cost per pound of meat
The variable $y$ represents the: cost per pound of cheese
The deli charges $\$4.50$ per pound of meat and $\$2.50$ per pound of cheese