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lbvjy [14]
2 years ago
5

A box of pencils is 5 1/4 inches wide. Seven pencils, laid side by side, take up 2 5/8 inches of the width. How many inches of t

he width of the box is not taken up by pencils? Show your reasoning. All the pencils have the same width. How wide is each pencil? Show your reasoning.
Mathematics
2 answers:
IRINA_888 [86]2 years ago
4 0

Answer:

3/8

Step-by-step explantion

.

Andre45 [30]2 years ago
3 0

Answer:   Width of box is not taken up by pencils =  2\dfrac58\text{ inches}

Width of each pencil =\dfrac38\text{ inches}

Step-by-step explanation:

Given: Width of pencil box = 5\dfrac14\text{ inches}=\dfrac{21}{4}\text{ inches}

Width of seven pencils = 2\dfrac58\text{ inches}=\dfrac{16+5}{8}\text{ inches}=\dfrac{21}{8}\text{ inches}

Width of box is not taken up by pencils =  Width of pencil box  - Width of seven pencils

\left \{ {{y=2} \atop {x=2}} \right. \dfrac{21}{4}-\dfrac{21}{8}\\\\=\dfrac{21\times2-21}{8}\\\\=\dfrac{21}{8}\text{ inches}=2\dfrac58\text{ inches}

Width of box is not taken up by pencils =  2\dfrac58\text{ inches}

Width of each pencil = (Width of seven pencils ) ÷ 7

=\dfrac{21}{8}\div7\\\\=\dfrac{21}{8}\times\dfrac17\\\\=\dfrac38\text{ inches}

Width of each pencil =\dfrac38\text{ inches}

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Grace [21]
<h3>Given :-</h3>

\\

  • x=y-1
  • x+2y=8

\\

<h3>To find:</h3>

\\

  • Value of x
  • Value of y

\\

<h3>Solution:-</h3>

Let say it is first equation:-

x=y-1. . . . (1)

and this is second equation:-

x+2y=8 . . . . (2)

\\  \\

Simplifying 1 equation:-

  • x = y - 1
  • x +1 = y
  • y = x + 1

Put this value of y in second equation.

\\

\dashrightarrow \sf \: x+2y=8

\\

\dashrightarrow \sf \: x+2(x + 1)=8

\\

\dashrightarrow \sf \: x+2x +2=8

\\  \\

\dashrightarrow \sf \: 3x +2=8

\\  \\

\dashrightarrow \sf \: 3x=8 - 2

\\  \\

\dashrightarrow \sf \: 3x=6

\\  \\

\dashrightarrow \sf \: x=6 \div 3

\\  \\

\dashrightarrow \sf \: x= \bf2

\\

to find value of y :-

y = x + 1

y = 2 + 1

y = 3

\\

verification:-

\\

1 equation:-

x = y - 1

put value of x and y

2 = 3 - 1

2 = 2

LHS = RHS

Hence verified!

\\

2 equation:-

\\

  • x+2y=8

put value of x and y

  • 2 + 2 × 3 = 8
  • 2 + 6 = 8
  • 8 = 8

LHS = RHS

Hence verified!

\\

Both equation verified!

.°. value of x and y is 2 and 3 respectively

7 0
2 years ago
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