If Student S has n pencils and Student R has four fewer, and Student T has twice as many as R, which expression represents T's pencils?

If Student S has n pencils and Student R has four fewer, and Student T has twice as many as R, which expression represents T's pencils?

• A. 2(n - 4)
• B. n + 4
• C. 2n - 4
• D. n/2

Answer: (A)

The key here is translating the relationships into an expression step by step. Student S has n pencils. Student R has four fewer than S, so R = n − 4. Student T has twice as many as R, so T = 2 × R. Substituting R gives T = 2 × (n − 4). That’s the expression for T’s pencils. (Expanding it would give 2n − 8, but the form 2(n − 4) directly reflects the described sequence: subtract 4 from S, then double the result.) The other forms don’t follow the described steps: adding four would not reflect R being four fewer than S, doubling S and then subtracting four would give 2n − 4, and halving S would give n/2.

The key here is translating the relationships into an expression step by step. Student S has n pencils. Student R has four fewer than S, so R = n − 4. Student T has twice as many as R, so T = 2 × R. Substituting R gives T = 2 × (n − 4). That’s the expression for T’s pencils. (Expanding it would give 2n − 8, but the form 2(n − 4) directly reflects the described sequence: subtract 4 from S, then double the result.)

The other forms don’t follow the described steps: adding four would not reflect R being four fewer than S, doubling S and then subtracting four would give 2n − 4, and halving S would give n/2.