Question
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.
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.
Answers
GPT-4o mini
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.**
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.**