Question store-
Store A sells raspberries for per pint and blackberries for per pint. Store B sells raspberries for per pint and blackberries for per pint. A certain purchase of raspberries and blackberries would cost at Store A or at Store B. How many pints of blackberries are in this purchase?
Store A sells raspberries for $ 5.50 per pint and blackberries for $ 3.00 per pint.
Hard-difficulty · SAT Math · Systems of Two Linear Equations — Elimination method. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
Choice C is correct. It’s given that store A sells raspberries for per pint and blackberries for per pint, and a certain purchase of raspberries and blackberries at store A would cost . It’s also given that store B sells raspberries for per pint and blackberries for per pint, and this purchase of raspberries and blackberries at store B would cost . Let represent the number of pints of raspberries and represent the number of pints of blackberries in this purchase. The equation represents this purchase of raspberries and blackberries from store A and the equation represents this purchase of raspberries and blackberries from store B. Solving the system of equations by elimination gives the value of and the value of that make the system of equations true. Multiplying both sides of the equation for store A by yields , or . Multiplying both sides of the equation for store B by yields , or . Subtracting both sides of the equation for store A, , from the corresponding sides of the equation for store B, , yields , or . Dividing both sides of this equationby yields . Thus, 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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