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?

Rationale

The store sold 10 two-packs of pens yesterday.

Let \( x \) represent the number of three-packs sold, which means the number of two-packs sold is \( 2x \). Each three-pack contains 3 pens, and each two-pack contains 2 pens. The total pens sold can be represented by the equation \( 2(2x) + 3x = 35 \). Solving this gives \( x = 5 \), leading to \( 2x = 10 \) for the two-packs sold.

A (5) CORRECT

This choice represents the number of three-packs sold, not the two-packs. Since the problem states that twice as many two-packs were sold compared to three-packs, this would not satisfy the condition of the total number of pens sold.

B (10) YOUR ANSWER

This is the correct number of two-packs sold. The calculations confirm that if \( x = 5 \) (three-packs), then \( 2x = 10 \) (two-packs), contributing correctly to the total of 35 pens when combined with the three-packs sold.

C (15) YOUR ANSWER

If 15 two-packs were sold, that would imply \( x = 7.5 \) for the three-packs, which is impossible in this context since the number of packs must be a whole number. Thus, this choice does not align with the requirements of the problem.

D (20) YOUR ANSWER

This option suggests that 20 two-packs were sold, leading to the conclusion that only \( x = -5 \) three-packs could have been sold, which is again impossible. This choice greatly exceeds the total pen count and violates the problem's constraints.

Conclusion

In summary, the store sold 10 two-packs of pens yesterday, consistent with the established relationship between the number of two-packs and three-packs. The calculations validate that the total number of pens sold equals 35 when combining both pack types correctly, confirming the accurate solution lies with the number of two-packs sold.

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?

The store sold 10 two-packs of pens yesterday.

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