MATH SOLVE

3 months ago

Q:
# Hez is making a bookcase the boards that are used to make the bookcase are 13/16 inch thick Hez found a board that is 1 1/4 inches thick by how much does Hez have to reduce the thickness of the new board to match the other boards of the bookcase

Accepted Solution

A:

Hez have to reduce the thickness of the new board by 35% to match the other boards of the bookcaseSolution: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%