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Algebra / Linear equations in two variables Difficulty: Easy

$3 a plus 4 b, equals 25$

A shipping company charged a customer $25 to ship some small boxes and some large boxes. The equation above represents the relationship between a, the number of small boxes, and b, the number of large boxes, the customer had shipped. If the customer had 3 small boxes shipped, how many large boxes were shipped?

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Explanation

Choice B is correct. It’s given that a represents the number of small boxes and b represents the number of large boxes the customer had shipped. If the customer had 3 small boxes shipped, then $a, equals 3$ . Substituting 3 for a in the equation $3 a, plus 4 b, equals 25$ yields $3 times 3, plus 4 b, equals 25$ or $9 plus 4 b, equals 25$ . Subtracting 9 from both sides of the equation yields $4 b equals 16$ . Dividing both sides of this equation by 4 yields $b equals 4$ . Therefore, the customer had 4 large boxes shipped.

Choices A, C, and D are incorrect. If the number of large boxes shipped is 3, then $b equals 3$ . Substituting 3 for b in the given equation yields $3 a, plus, 4 times 3, equals 25$ or $3 a, plus 12, equals 25$ . Subtracting 12 from both sides of the equation and then dividing by 3 yields $a, equals thirteen thirds$ . However, it’s given that the number of small boxes shipped, a, is 3, not $thirteen thirds$ , so b cannot equal 3. Similarly, if $b equals 5$ or $b equals 6$ , then $a, equals five thirds$ or $a, equals one third$ , respectively, which is also not true.