Question: Store A sells raspberries for $5.50 per pint and blackberries for $3.00 per pint. Store B sells raspberries for $6.50 per pint and blackberries for $8.00 per pint. A certain purchase of raspberries and blackberries would cost $37.00 at Store A or $66.00 at Store B. How many pints of blackberries are in this purchase?
1. **State the problem:** We need to find the number of pints of blackberries in a purchase where the total cost is $37.00 at Store A and $66.00 at Store B.
2. **Define variables:** Let $r$ be the number of pints of raspberries and $b$ be the number of pints of blackberries.
3. **Write the system of equations based on prices:**
Store A: $$5.50r + 3.00b = 37$$
Store B: $$6.50r + 8.00b = 66$$
4. **Solve the system:**
From Store A equation, isolate $r$:
$$5.50r = 37 - 3b$$
$$r = \frac{37 - 3b}{5.50}$$
5. **Substitute $r$ into Store B equation:**
$$6.50 \times \frac{37 - 3b}{5.50} + 8b = 66$$
6. **Multiply both sides by 5.50 to clear denominator:**
$$6.50(37 - 3b) + 8b \times 5.50 = 66 \times 5.50$$
$$6.50 \times 37 - 6.50 \times 3b + 44b = 363$$
Calculate constants:
$$240.5 - 19.5b + 44b = 363$$
7. **Combine like terms:**
$$240.5 + (44b - 19.5b) = 363$$
$$240.5 + 24.5b = 363$$
8. **Isolate $b$:**
$$24.5b = 363 - 240.5$$
$$24.5b = 122.5$$
$$b = \frac{122.5}{24.5}$$
9. **Simplify fraction:**
$$b = 5$$
10. **Answer:** There are **5 pints** of blackberries in the purchase.
**Final answer: B 5**