Question

A picture framer has a thin board 10 1/2 feet long. The framer notices that 2 3/8 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

1. Find how many of the board can be used for picture frames:

`10(1)/(2)-2(3)/(8)=(21)/(2)-(19)/(8)=(21\cdot 4-19)/(8)=(65)/(8)\ ft.`

2. Each picture frame needs
`1(2)/(3)=(5)/(3)` feet of the board, then the farmer can complete

`(65)/(8):(5)/(3)=(65)/(8)\cdot (3)/(5)=(39)/(8)=4(7)/(8)`

picture frames.

Answer: at most he can complete 4 picture frames.