Hez have to reduce the thickness of the new board by 35% to match the other boards of the bookcase
Solution:
The boards that are used to make the bookcase are [tex]\frac{13}{16}[/tex] inch thick
Hez found a board that is [tex]1\frac{1}{4}[/tex] inches thick
Let us consider that he has to reduce the n% of board
Then, thickness – n% of thickness = required thickness
[tex]1 \frac{1}{4}-n \% \text { of } 1 \frac{1}{4}=\frac{13}{16}[/tex]
On solving we get,
[tex]1 \frac{1}{4}(1-\mathrm{n} \%)=\frac{13}{16}[/tex]
[tex]\frac{1 \times 4+1}{4}(1-n \%)=\frac{13}{16}[/tex]
[tex]\frac{5}{4}(1-\mathrm{n} \%)=\frac{13}{16}[/tex]
On simplification,
[tex]\begin{array}{l}{1-n \%=\frac{13}{20}} \\\\ {n \%=\frac{20-13}{20}} \\\\ {\frac{n}{100}=\frac{7}{20}} \\\\ {\frac{n}{5}=\frac{7}{1}} \\\\ {n=7 \times 5} \\\\ {n=35}\end{array}[/tex]
Hence, he has to reduce the board by 35%
