Question

Question:-
After traveling a distance of 32 $\frac{4}{5}$km, Amera found that she is still to cover $\frac{5}{7}$ of the whole distance. what is the total distance covered by amera.
•This is very easy question but the answer should come 114$\frac{4}{5}$ km
• Note:-follow app rules dont copy it from any web answer on your on
•Take your time to answer
•Thanks in advance for Answer ​

Answer 1

Let Amera has to cover x km distance

Then, she still has to cover 5x/7 distance

she covered (x- 5x/7)-2x/7 distance

So,

=> 2x/7=164/5

=> x= 114.8 kms

so, the total distance is 114.8 kms

Answer 2

Answer:

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$\sf Total \ Distance = 114\dfrac{4}{5} \ km$

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Step-by-step explanation:

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Given;

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$\sf \dashrightarrow \textsf{Distance covered by Amera} = \sf 32\dfrac{4}{5} \ km$

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$\sf \dashrightarrow \textsf{Part of the total distance that needs to be covered} \\\textsf{ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ in order to cover the full distance}$  $= \sf \dfrac{5}{7} \times Whole \ Distance$

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Let the Whole distance be "D", therefore;

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$\sf \dashrightarrow \textsf{Part of the total distance that needs to be covered} \\\textsf{ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ in order to cover the full distance}$  $= \sf \dfrac{5}{7}D$

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We know that;

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$\dashrightarrow \textsf{ Distance covered} \ + \textsf{ Part of the total distance} \\\textsf{\ \ \ \ \ \ \ \ \ \ By Amera \ \ \ \ \ \ \ \ \ \ that needs to be covered to} \ \ \sf = Total \ Distance \\\textsf{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ complete the whole distance}$

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On substituting the values we get;

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$\sf \dashrightarrow \ 32\dfrac{4}{5} \ + \ \dfrac{5D}{7} \ = \ D$

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$\sf \dashrightarrow \ 32\dfrac{4}{5} \ = \ D \ - \dfrac{5D}{7}$

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On converting the mixed fractions to improper fractions we get;

• [In-order to do so, we'll multiply the denominator and the whole number, and add the product to the numerator]

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$\sf \dashrightarrow \ \dfrac{(32 \times 5) + 4}{5} \ = \ D \ - \ \dfrac{5D}{7}$

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$\sf \dashrightarrow \ \dfrac{(160) + 4}{5} \ = \ D \ - \ \dfrac{5D}{7}$

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$\sf \dashrightarrow \ \dfrac{164}{5} \ = \ D \ - \ \dfrac{5D}{7}$

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On taking LCM in the RHS we get;

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$\sf \dashrightarrow \ \dfrac{164}{5} \ = \ \dfrac{7D - 5D}{7}$

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$\sf \dashrightarrow \ \dfrac{164}{5} \ = \ \dfrac{2D}{7}$

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On transposing 7 to the LHS we get;

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$\sf \dashrightarrow \ \dfrac{164 \times 7}{5} \ = \ \dfrac{2D}{1}$

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$\sf \dashrightarrow \ \dfrac{1148}{5} \ = \ \dfrac{2 \times D}{1}$

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On transposing 2 to the LHS we get;

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$\sf \dashrightarrow \ \dfrac{1148}{5 \times 2} \ = \ D$

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On dividing 1148 and 2 we get;

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$\sf \dashrightarrow \ \dfrac{574}{5} \ = \ D$

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On converting the improper fraction to a mixed fraction we get; [Refer to the attachment]

• To convert an improper fraction to a mixed fraction, divide the numerator by the denominator, the resulting quotient will be the whole number, the remainder will be the numerator, and the denominator will remain the same (original).

‎‎

$\sf \dashrightarrow D = 114\dfrac{4}{5} \ km.$

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Therefore, the total distance covered by Amera is 114 ⁴/₅ km.

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[Please view the answer on the website if the lines look cluttered on the app]