Katrina is building a deck. She cuts 3 lengths of wood from a 72-inch board. The first length is 30 3/4 inches. The second length is 12 1/4 inches. And the third length is 16 1/4 inches. How much of the original board remains after Katrina makes her cuts? help me pleaz !!!!!!!!

first add them together
30 and 3/4+12 and 1/4+ 16 and 1/4=30+3/4+12+1/4+16+1/4 =30+12+16+3/4+1/4+1/4=58+1+1/4=59+1/4=59 and 1/4
subtract from 72
72-59 and 1/4=72-(59+1/4)=72-59-1/4=71+1-59-1/4= 71-59+1-1/4= 71-59+4/4-1/4=12+3/4

the legnth left is 12 and 3/4 inches

Answer Link

calculista calculista · Answer 2 · 2018-10-10T17:58:15-04:00

Let

x-------> remainder of the original board

we know that

[tex]72=30\frac{3}{4} +12\frac{1}{4}+16\frac{1}{4} +x[/tex] ------> equation [tex]1[/tex]

Convert mixed numbers to an improper fractions

[tex]30\frac{3}{4}=\frac{30*4+3}{4}=\frac{123}{4}[/tex]

[tex]12\frac{1}{4}=\frac{12*4+1}{4}=\frac{49}{4}[/tex]

[tex]16\frac{1}{4}=\frac{16*4+1}{4}=\frac{65}{4}[/tex]

Substitute the values in the equation [tex]1[/tex] and solve for x

[tex]72=\frac{123}{4} +\frac{49}{4}+\frac{65}{4} +x[/tex]

[tex]72=\frac{237}{4} +x[/tex]

solve for x

[tex]x=72-\frac{237}{4}[/tex]

[tex]x=72-59.25[/tex]

[tex]x=12.75\ inches[/tex]

convert to mixed number

[tex]x=12.75\ inches=12+0.75=12+\frac{3}{4}=12\frac{3}{4}\ inches[/tex]

therefore

the answer is

[tex]12\frac{3}{4}\ inches[/tex]