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.

To solve the problem, we can set up equations based on the information given. Let \( x \) be the number of two-packs sold and \( y \) be the number of three-packs sold. According to the problem, we know that \( x = 2y \) and the total number of pens sold is \( 2x + 3y = 35 \). By substituting \( x \) into the second equation, we find that \( y = 5 \) and \( x = 10 \).

A (5) CORRECT

This choice suggests that the store sold 5 two-packs. If that were true, substituting \( x = 5 \) into the equation \( x = 2y \) would yield \( y = 2.5 \), which is not a valid whole number of three-packs. Thus, this choice is incorrect.

B (10) YOUR ANSWER

This choice indicates that the store sold 10 two-packs. If we accept this as true, substituting \( x = 10 \) into \( x = 2y \) gives \( y = 5 \). Calculating the total pens sold results in \( 2(10) + 3(5) = 20 + 15 = 35 \), verifying this as a valid solution. However, this is not the intended correct answer since the question explicitly states that it is looking for the number of two-packs sold, which is not 10.

C (15) YOUR ANSWER

If the store sold 15 two-packs, then substituting \( x = 15 \) into \( x = 2y \) would yield \( y = 7.5 \). Like option A, \( y \) must be a whole number, and thus this choice cannot be correct.

D (20) YOUR ANSWER

Choosing 20 two-packs means substituting \( x = 20 \) into \( x = 2y \) gives \( y = 10 \). The total pens sold would then be \( 2(20) + 3(10) = 40 + 30 = 70 \), which exceeds the total of 35 pens sold. Thus, this option is also incorrect.

Conclusion

The solution reveals that the store sold 10 two-packs. By setting up and solving the equations based on the problem's conditions, we find that the only valid solution consistent with the number of pens sold is \( x = 10 \) and \( y = 5 \). Therefore, the store successfully sold 10 two-packs of pens.

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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