Morgan runs a farm stand that sells apples and blueberries. Yesterday Morgan sold 20 pounds of apples and 50 pounds of blueberries for a total revenue of $160. Today she sold 38 pounds of apples and 10 pounds of blueberries for a total revenue of $134. Determine the price of each pound of apples and the price of each pound of blueberries.(1 point)

Responses

Apples cost $3/lb and blueberries cost $2/lb.
Apples cost $3/lb and blueberries cost $2/lb.

Apples cost $2/lb and blueberries cost $3/lb.
Apples cost $2/lb and blueberries cost $3/lb.

Apples cost $4/lb and blueberries cost $1.60/lb.
Apples cost $4/lb and blueberries cost $1.60/lb.

Apples cost $5/lb and blueberries cost $2/lb.
Apples cost $5/lb and blueberries cost $2/lb.

1 answer

Let \( a \) be the price per pound of apples and \( b \) be the price per pound of blueberries.

From the information given, we can set up the following system of equations based on Morgan's sales:

  1. From yesterday's sales: \[ 20a + 50b = 160 \]

  2. From today's sales: \[ 38a + 10b = 134 \]

Now, we can simplify these equations:

From the first equation, let's simplify it: \[ 20a + 50b = 160 \quad \text{(dividing the entire equation by 10)} \] \[ 2a + 5b = 16 \tag{1} \]

From the second equation: \[ 38a + 10b = 134 \quad \text{(dividing the entire equation by 2)} \] \[ 19a + 5b = 67 \tag{2} \]

Now we can solve this system of equations. We can subtract equation (1) from equation (2) to eliminate \( b \):

First, rewrite both equations: \[ 2a + 5b = 16 \tag{1} \] \[ 19a + 5b = 67 \tag{2} \]

Now subtract equation (1) from equation (2): \[ (19a + 5b) - (2a + 5b) = 67 - 16 \] \[ 17a = 51 \] \[ a = 3 \]

Now that we know the price of apples, we can plug \( a \) back into equation (1) to find \( b \). Using equation (1): \[ 2(3) + 5b = 16 \] \[ 6 + 5b = 16 \] \[ 5b = 10 \] \[ b = 2 \]

Thus, the price per pound of apples is \( 3 \) dollars, and the price per pound of blueberries is \( 2 \) dollars.

To summarize:

  • Apples cost \( \text{$}3/\text{lb} \)
  • Blueberries cost \( \text{$}2/\text{lb} \)

So the correct response is: Apples cost $3/lb and blueberries cost $2/lb.