Juan subtracted 3 from a certain number n and then multiplied the difference by 2. Marta multiplied the same number n by 8 and then subtracted 11 from the product. Both Juan and Marta got the same result. What is the value of n?

Rationale

Juan and Marta both arrived at the same result when n equals 5 1/2.

To solve the problem, we set up equations based on the operations performed by Juan and Marta. Juan's operation leads to the equation \(2(n - 3)\), while Marta's operation results in \(8n - 11\). Setting these equal to each other and solving yields \(n = 5.5\).

A (3/4) YOUR ANSWER

If we substitute \(n = 3/4\) into Juan's equation, we get \(2(3/4 - 3) = 2(3/4 - 12/4) = 2(-9/4) = -9/2\). For Marta, \(8(3/4) - 11 = 6 - 11 = -5\). Since \(-9/2\) does not equal \(-5\), this choice is incorrect.

B (5 1/2) CORRECT

Substituting \(n = 5.5\) into Juan's calculation gives \(2(5.5 - 3) = 2(2.5) = 5\). For Marta, \(8(5.5) - 11 = 44 - 11 = 33\). Thus, both operations yield the same result, confirming that this is the correct answer.

C (1/3) YOUR ANSWER

For \(n = 1/3\), Juan calculates \(2(1/3 - 3) = 2(1/3 - 9/3) = 2(-8/3) = -16/3\). Marta computes \(8(1/3) - 11 = 8/3 - 11 = 8/3 - 33/3 = -25/3\). Since \(-16/3\) is not equal to \(-25/3\), this choice is incorrect.

D (1.2) YOUR ANSWER

Substituting \(n = 1.2\) into Juan's equation results in \(2(1.2 - 3) = 2(-1.8) = -3.6\). For Marta, \(8(1.2) - 11 = 9.6 - 11 = -1.4\). Since \(-3.6\) does not equal \(-1.4\), this choice is also incorrect.

Conclusion

The correct solution to the problem is \(n = 5 1/2\), as this is the only value that satisfies the equations derived from Juan's and Marta's operations. Analyzing each incorrect option demonstrates that they do not yield equal results, reinforcing that only \(5 1/2\) fulfills the condition

Juan subtracted 3 from a certain number n and then multiplied the difference by 2. Marta multiplied the same number n by 8 and then subtracted 11 from the product. Both Juan and Marta got the same result. What is the value of n?

Juan and Marta both arrived at the same result when n equals 5 1/2.

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