A picture framer has a board 10 1/12 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?

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RenatoMatticeid RenatoMatticeid · Answer 1

Answer: There are atmost 4 picture frames can be made.

Step-by-step explanation:

Since we have given that

Length of board is given by

[tex]10\frac{1}{12}\text{ feet}[/tex]

Length of board is scratched and cannot be used is given by

[tex]2\frac{3}{8}\text{ feet}[/tex]

Rest of board will be used to make small picture frames is given by

[tex]\frac{121}{12}-\frac{19}{8}\\\\=\frac{242-57}{24}\\\\=\frac{185}{24}\text{ feet}[/tex]

Length of board needed for each picture frame is given by

[tex]1\frac{2}{3}=\frac{5}{3}\text{ feet}[/tex]

So, Number of complete picture frames can be made is given by

[tex]\frac{\frac{185}{24}}{\frac{5}{3}}\\\\=\frac{185\times 3}{24\times 5}\\\\=\frac{37}{8}\\\\=4.65[/tex]

∴ There are atmost 4 picture frames can be made.