Let's denote the number of pounds of apples purchased as \( x \).
For David's orchard:
- For the first 10 pounds, the cost is $2 per pound, so the cost for the first 10 pounds is \( 10 \times 2 = $20 \).
- For each additional pound beyond the first 10, the cost is $1 per pound. So, for the additional \( x - 10 \) pounds, the cost is \( (x - 10) \times 1 = x - 10 \) dollars.
For Pamela's orchard:
- There's a $10 entry fee, and then for the first 10 pounds, the cost is $1.50 per pound. So, the cost for the first 10 pounds is \( 10 \times 1.50 = $15 \).
- For each additional pound beyond the first 10, the cost is $0.75 per pound. So, for the additional \( x - 10 \) pounds, the cost is \( (x - 10) \times 0.75 = 0.75x - 7.5 \) dollars.
Setting up the equation for the total cost being equal:
\[ 20 + (x - 10) = 10 + 15 + (0.75x - 7.5) \]
Now, let's solve for \( x \):
\[ 20 + x - 10 = 25 + 0.75x - 7.5 \]
\[ x + 10 = 17.5 + 0.75x \]
\[ 0.25x = 7.5 \]
\[ x = \frac{7.5}{0.25} \]
\[ x = 30 \]
So, they will be equal at 30 pounds.
