If a job requires 400 linear feet of fabric and 400 feet of top rail, how many pieces are needed if top rail comes in 21-foot lengths?

If a job requires 400 linear feet of fabric and 400 feet of top rail, how many pieces are needed if top rail comes in 21-foot lengths?

• A. 19
• B. 17
• C. 20
• D. 22

Answer: (C)

The key idea is buying fixed-length pieces to meet a required total. Top rail comes in 21-foot pieces, and you need 400 feet. 400 divided by 21 equals about 19.05, but you can’t buy a fraction of a piece. So you must round up to 20 pieces. That gives 20 × 21 = 420 feet, which covers the 400-foot requirement with 20 feet of extra waste. Using only 19 pieces would give 399 feet, not enough. So the minimum number of pieces is 20.

The key idea is buying fixed-length pieces to meet a required total. Top rail comes in 21-foot pieces, and you need 400 feet. 400 divided by 21 equals about 19.05, but you can’t buy a fraction of a piece. So you must round up to 20 pieces. That gives 20 × 21 = 420 feet, which covers the 400-foot requirement with 20 feet of extra waste. Using only 19 pieces would give 399 feet, not enough. So the minimum number of pieces is 20.