11. 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?
Answer: B
The value of n is 5 1/2.
Juan's calculation results in the expression 2(n - 3), while Marta’s calculation gives us 8n - 11. Setting these equal to each other leads to solving for n, which reveals that n equals 5 1/2.
A) 3/4
This option is incorrect because substituting n = 3/4 into Juan's expression yields 2(3/4 - 3) = 2(-9/4) = -9/2, while Marta's calculation gives 8(3/4) - 11 = 6 - 11 = -5. These results do not match.
B) 5 1/2
This option is correct. If we substitute n = 5 1/2 into Juan's expression, we have 2(5.5 - 3) = 2(2.5) = 5. For Marta, 8(5.5) - 11 = 44 - 11 = 33. Since both yield the same final result, this confirms that n = 5 1/2 is accurate.
C) 1/3
This option is incorrect. Substituting n = 1/3 into Juan's expression results in 2(1/3 - 3) = 2(-8/3) = -16/3. For Marta, 8(1/3) - 11 = 8/3 - 11 = -25/3. The outputs from both calculations do not match.
D) 1.2
This option is also incorrect. When substituting n = 1.2 into Juan's expression, we calculate 2(1.2 - 3) = 2(-1.8) = -3.6. For Marta, 8(1.2) - 11 equals 9.6 - 11 = -1.4. The results from Juan and Marta do not equal each other.
Conclusion
The calculations confirm that the only value of n that satisfies both Juan's and Marta's equations is 5 1/2. All other options fail to produce matching results when plugged into both individuals' calculations, solidifying option B as the definitive answer.