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zepelin [54]
3 years ago
5

María compró 78 metros de cuerda, ella dividió en 6 partes iguales la cuerda el día martes 8 de mayo ¿Cuántos metros mide cada t

rozo? *
a) Cada trozo mide 312m
c) Cada trozo mide 13m
d) cada trozo mite 92m
b) Cada trozo mide 9m y 75cm
Mathematics
1 answer:
barxatty [35]3 years ago
6 0

Answer:

The length of each piece is 13 m.

Step-by-step explanation:

Maria bought 78 meters of rope, she divided the rope into 6 equal parts on Tuesday, May 8, How many meters is each piece?  

a) Each piece measures 312m

c) Each piece measures 13m

d) each piece mites 92m

b) Each piece measures 9m and 75cm

Total length, L =  78 m

Number of pieces, n = 6

length of each piece,

d = L/n = 78/6 = 13 m

So, the correct option is (c).  

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Divide through everything by <em>b</em> :

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Since <em>a/b</em> < <em>c/d</em>, it follows that

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Multiply through everything on the right side by <em>b/d</em> to get

\dfrac{a+c}{b+d} < \dfrac{\dfrac{bc}{d^2}+\dfrac cd}{\dfrac bd+1} = \dfrac{\dfrac cd\left(\dfrac bd+1\right)}{\dfrac bd+1} = \dfrac cd

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For the other side, you can do something similar and divide through everything by <em>d</em> :

\dfrac{a+c}{b+d} = \dfrac{\dfrac ad + \dfrac cd}{\dfrac bd + 1}

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Then

\dfrac{a+c}{b+d} > \dfrac{\dfrac ab + \dfrac{ad}{b^2}}{1 + \dfrac db} = \dfrac{\dfrac ab\left(1+\dfrac db\right)}{1 + \dfrac db} = \dfrac ab

and so (<em>a</em> + <em>c</em>)/(<em>b</em> + <em>d</em>) > <em>a/b</em>.

Then together we get the desired inequality.

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