Answer:
The width of the spacing between each board is [tex]\frac{21}{56}[/tex] inches.
Step-by-step explanation:
Given: Each board [tex]9\frac{1}{4} inches[/tex].
Let's convert the mixed number [tex]9\frac{1}{4} inches[/tex] to improper fraction.
[tex]9\frac{1}{4} = \frac{37}{4}[/tex]
Total width of 15 boards = [tex]15 . \frac{37}{4} = 138 \frac{3}{4}[/tex] inches
Now we have to find the total space between the boards.
The total space = 144 - [tex]138 \frac{3}{4}[/tex]
The total space = [tex]5 \frac{1}{4}[/tex]
There 14 equal spaces between each board.
To find the width of spacing between each board, we need to divide [tex]5 \frac{1}{4}[/tex] by 14.
The width of spacing between each board = [tex]\frac{5\frac{1}{4} }{14}[/tex]
Now we can convert the mixed number to improper and multiply with the reciprocal of 14.
The reciprocal of 14 is [tex]\frac{1}{14}[/tex]
= [tex]\frac{21}{4} . \frac{1}{14} = \frac{21}{56}[/tex]
Therefore, the width of the spacing between each board is [tex]\frac{21}{56}[/tex] inches.
The spacing inbetween successive boards can be obtained using arithmetic expression. Hence, the between the boards is [tex]\frac{3}{8} [/tex]
Let the size per spacing = n
We could write the expression thus :
[tex] (\frac{555}{4}) + 14n = 144 [/tex]
[tex]14n = 144 - \frac{555}{4} [/tex]
[tex]14n = \frac{576 - 555}{4} = \frac{21}{4} [/tex]
[tex]14n= \frac{21}{4} [/tex]
[tex]14n \times 4 = 21[/tex]
[tex] n = \frac{21}{56} = \frac{3}{8} inches [/tex]
Therefore, the spacing inbetween successive boards is [tex]\frac{3}{8} [/tex]
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