SAT Question 1e11190a: Answer, Explanation & Desmos Solution

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?

Difficulty:Hard

$4$

$5$

$8$

$12$

Explanation

Correct answer: B.

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.

Desmos solution:

Note: r represents pints of raspberries and b represents pints of blackberries in the purchase.

Enter in Desmos:

$[5.50 r + 3 b, 6.50 r + 8 b] \sim [37, 66]$

Reviewed and rewritten by CookSAT

Why the other choices are wrong

Choice A

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.

Choice C

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 $5.50 r + 3.00 b = 37.00$ 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

Choice D is incorrect. This is the number of pints of raspberries, not blackberries, in the purchase.

Student discussion

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Translation approach

SAT Question 1e11190a: Systems of Linear Equations answer and explanation with Desmos solution

Explanation

Enter in Desmos:

Why the other choices are wrong

Student discussion