28. A store sells pens in packs of two or three. Yesterday the store sold 35 pens. It sold twice as many two-packs as three-packs. How many two-packs of pens did the store sell yesterday?
Answer: A
The store sold 5 two-packs of pens yesterday.
To find the number of two-packs sold, we set up the problem based on the information given. Let \( x \) be the number of three-packs sold. Then, the number of two-packs sold is \( 2x \). The total number of pens sold can be expressed as \( 2(2x) + 3x = 35 \), leading to the solution that \( x = 5 \) and thus \( 2x = 10 \).
A) 5
Option A is correct as it represents the number of two-packs sold. Given that the store sold twice as many two-packs as three-packs, we find that if \( x \) (the number of three-packs) is 5, then \( 2x \) equals 10, which confirms that the total number of pens sold is indeed 35.
B) 10
Option B is incorrect because it suggests that the store sold 10 two-packs. If this were true, the number of three-packs would need to be 5 (since \( 10 = 2(5) \)), leading to a total of \( 10 \times 2 + 5 \times 3 = 20 + 15 = 35 \), which does not align with the relationship given in the problem.
C) 15
Option C is incorrect as it implies that 15 two-packs were sold. If the store sold 15 two-packs, the total number of three-packs sold would be 7.5, which is impossible since the number of packs must be a whole number. Therefore, this option cannot be correct.
D) 20
Option D is incorrect because it indicates that the store sold 20 two-packs. If this were the case, the number of three-packs sold would need to be 10 (since \( 20 = 2(10) \)), leading to a total of \( 20 \times 2 + 10 \times 3 = 40 + 30 = 70 \), which exceeds the total of 35 pens sold.
Conclusion
The correct answer is A, as it accurately reflects the calculations derived from the problem's constraints. The other options fail to meet the requirements set by the relationships between the number of two-packs and three-packs sold, making them invalid choices.