Question store-

1.4 Systems of Two Linear Equations - Elimination method
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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?

A.

4

B.

5

C.

8

D.

12

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 $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 5.50r6.5+3.00b6.5=37.006.5, or 35.75r+19.5b=240.5. Multiplying both sides of the equation for store B by 5.5 yields 6.50r5.5+8.00b5.5=66.005.5, 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 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.