Question

a wire is cut into two pieces. The longer piece is 147 cm longer than three times the shorter piece. The shorter piece is 2/11 of the wire. Find the length of the wire

Answer 1

Step-by-step explanation:

147+3s = l

s =2/11(l+s)

s = 2(147+3s+s)/11

11s = 2(147+4s) = 294+8s

3s = 294

s= 98

l = 147+3×98 = 441

length of wire = l+s = 441+98 = 539 cm

Answer 2

Question :-

• A wire is cut into two pieces. The longer piece is 147 cm longer than three times the shorter piece. The shorter piece is 2/11 of the wire. Find the length of the wire.

Answer

Given :-

• A wire is cut into two pieces. The longer piece is 147 cm longer than three times the shorter piece. The shorter piece is 2/11 of the wire.

To Find :-

• The length of the wire.

Solution:-

Let length of wire be 'x' cm.

$\bf \:Shorter \: piece = \dfrac{2}{11} x \: cm$

$\bf \:Longer \: piece = 3 \times Shorter \: piece + 147$

$\bf\implies \:Longer \: piece = 3 \times \dfrac{2}{11} x + 147$

$\bf\implies \:Longer \: piece = \dfrac{6}{11} x + 147$

❥ Now, Length of wire = Length of Shorter piece + Length of Longer piece

$\bf\implies \:x = \dfrac{2x}{11} + \dfrac{6x}{11} + 147$

$\bf\implies \:x - \dfrac{2x}{11} - \dfrac{6x}{11} = 147$

$\bf\implies \:\dfrac{11x - 2x - 6x}{11} = 147$

$\bf\implies \:\dfrac{3x}{11} = 147$

$\bf\implies \:x = 147 \times \dfrac{11}{3}$

$\bf\implies \:x = 539 \: cm$

$\bf \:⇛ Length \: of wire = 539 \: cm$

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$\bf\large \underbrace\red{Verification}$

$\bf \:Shorter \: piece = \dfrac{2}{11} x$

$\bf\implies \:Shorter \: piece = \dfrac{2}{11} \times 539 = 98 \: cm$

$\bf \:Longer \: piece = \dfrac{6x}{11} + 147$

$\bf\implies \:Longer \: piece = \dfrac{6}{11} \times 539 + 147$

$\bf\implies \:Longer \: piece = 441 \: cm$

❥ Now, Length of wire = Length of Shorter piece + Length of Longer piece

$\bf \:⇛ Length \: of \: wire = 98 + 441 = 539 \: cm.$

$\large{\boxed{\boxed{\bf{Hence \: verified}}}}$

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