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