Store A sells raspberries for $ 5.50 per pint and blackberries for $ 3.00 per pint. Store B sells raspberries

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?

Accepted Answer

Choice C is correct. It&rsquo;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&rsquo;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 . 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 . 5 b = 122 . 5 . Dividing both sides of this equationby 24.5 yields b = 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.

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