Question

Which equation represents the sentence 'five more than three times the number is one-third more than the sum of the number and itself'?

1) 3n + 5 = (n + n) + 1/3
2) 5(3n) = 13n
3) 3n + 5 = 1/3(n + n)
4) 5(3n) = 13(n + n)

Answer 1

The correct mathematical representation of the sentence 'five more than three times the number is one-third more than the sum of the number and itself' should be '3n + 5 = (4/3)n'. Option 3 is the closest, but none of the provided options correctly represent the equation. Therefore, none of the options is correct.

Step-by-step explanation:

The student's question asks which equation represents the sentence 'five more than three times the number is one-third more than the sum of the number and itself.' To translate this into a mathematical equation, let's denote the number as n. 'Three times the number' is 3n, and 'five more than three times the number' is 3n + 5. The 'sum of the number and itself' is n + n or 2n. 'One-third more than the sum of the number and itself' can be represented as 2n + (1/3)2n which simplifies to (4/3)n. Therefore, the equation that represents the original sentence is 3n + 5 = (4/3)n. Among the given options, option 3) 3n + 5 = 1/3(n + n) is the closest to our equation, but it has a mistake in the representation of one-third more than the sum. The correct right-hand side should be multiplied by (4/3), not added by (1/3).