Question

A picture framer has a thin board 101/2 feet long.The farmer notices that 23/8 feet of the board is scratched and cannot be used.The rest of the board will be used to make small picture frames. Each picture frame needs 1 2/3 feet of the board.At most, how many complete picture frames can be made?

Answer 1

101/2 is 50 1/2
23/8 is 2 7/8
50 1/2 - 2 7/8 = 47 5/8
47 5/8 / 1 2/3 = 27.69, to the nearest hundredth
Since he can't make fractions of picture frame, the answer is 27

Answer 2

The farmer notices that 23/8 feet of the board with length 101/2 feet is scratched and cannot be used. Then left

`(101)/(2)-(23)/(8)=(404-23)/(8)=(381)/(8)` feet.

Each picture frame needs 1 2/3 feet of the board. Then the farmer can make 28 complete picture frames, because

`(381)/(8):(5)/(3) = (381)/(8)\cdot (3)/(5)=(1143)/(40)=28.575.`

Answer: 28 complete picture frames