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?

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Accepted Answer

Key Explanation: Choice C is correct. It’s given that store A sells raspberries for $5.50 per pint and blackberries for $3.00 per pint, and a certain purchase of raspberries and blackberries at store A would cost $37.00. It’s also given that store B sells raspberries for $6.50 per pint and blackberries for $8.00 per pint, and this purchase of raspberries and blackberries at store B would cost $66.00. Let r represent the number of pints of raspberries and b represent the number of pints of blackberries in this purchase. The equation 5.50r + 3.00b = 37.00 represents this purchase of raspberries and blackberries from store A and the equation 6.50r + 8.00b = 66.00 represents this purchase of raspberries and blackberries from store B. Solving the system of equations by elimination gives the value of r and the value of b that make the system of equations true. Multiplying both sides of the equation for store A by 6.5 yields (5.50r)(6.5) + (3.00b)(6.5) = (37.00)(6.5), or 35.75r + 19.5b = 240.5. Multiplying both sides of the equation for store B by 5.5 yields (6.50r)(5.5) + (8.00b)(5.5) = (66.00)(5.5), or 35.75r + 44b = 363. Subtracting both sides of the equation for store A, 35.75r + 19.5b = 240.5, from the corresponding sides of the equation for store B, 35.75r + 44b = 363, yields (35.75r − 35.75r) + (44b − 19.5b) = (363 − 240.5), or 24.5b = 122.5. Dividing both sides of this equation by 24.5 yields b = 5. Thus, 5 pints of blackberries are in this purchase. Distractor Explanations: Choices A and B are incorrect and may result from conceptual or calculation errors. Choice D is incorrect. This is the number of pints of raspberries, not blackberries, in the purchase.

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