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Algebra / Systems of two linear equations in two variables Difficulty: Hard

Store A sells raspberries for $dollar sign 5.50$ per pint and blackberries for $dollar sign 3.00$ per pint. Store B sells raspberries for $dollar sign 6.50$ per pint and blackberries for $dollar sign 8.00$ per pint. A certain purchase of raspberries and blackberries would cost $dollar sign 37.00$ at Store A or $dollar sign 66.00$ at Store B. How many pints of blackberries are in this purchase?

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Explanation

Choice C is correct. It’s given that store A sells raspberries for $dollar sign 5 period 50$ per pint and blackberries for $dollar sign 3 period 00$ per pint, and a certain purchase of raspberries and blackberries at store A would cost $dollar sign 37 period 00$ . It’s also given that store B sells raspberries for $dollar sign 6 period 50$ per pint and blackberries for $dollar sign 8 period 00$ per pint, and this purchase of raspberries and blackberries at store B would cost $dollar sign 66 period 00$ . Let $r$ represent the number of pints of raspberries and $b$ represent the number of pints of blackberries in this purchase. The equation $5.50 r + 3.00 b = 37.00$ represents this purchase of raspberries and blackberries from store A and the equation $6.50 r + 8.00 b = 66.00$ 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 $(5.50 r) (6.5) + (3.00 b) (6.5) = (37.00) (6.5)$ , or $35.75 r + 19.5 b = 240.5$ . Multiplying both sides of the equation for store B by $5.5$ yields $(6.50 r) (5.5) + (8.00 b) (5.5) = (66.00) (5.5)$ , or $35.75 r + 44 b = 363$ . Subtracting both sides of the equation for store A, $35.75 r + 19.5 b = 240.5$ , from the corresponding sides of the equation for store B, $35.75 r + 44 b = 363$ , yields $(35.75 r - 35.75 r) + (44 b - 19.5 b) = (363 - 240.5)$ , or $24 period 5 b equals 122 period 5$ . Dividing both sides of this equationby $24.5$ yields $b equals 5$ . Thus, $5$ pints of blackberries are in
this purchase.

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.