Question

a carton contains three types of fruits weighting 36 1/3kg in all out of total fruit guava weight 9 4/9kg grapes weight 7 11/15 kg and rest of the weight is of orange how much do the orange weight?​

Answer 1

Answer:

24 ⁷/₄₅ kg

Step-by-step explanation:

As per the provided information in the given question, we have :

• Total weight = 36 ¹/₃ kg
• Wight of guava = 4 ⁴/₉ kg
• Weight of grapes = 7 ¹¹/₁₅ kg
• Rest of the weight is of oranges.

Let us suppose the weight of the oranges as x kg.

The sum of all the fruits' weight will be the total weight of carton. Writing it in the form of a linear equation,

$\longrightarrow \sf{\quad { 36\dfrac{1}{3} =x + 4\dfrac{4}{9} + 7\dfrac{11}{15} }}$

Firstly, convert the mixed fraction into simple fraction.

$\longrightarrow \sf{\quad { \dfrac{109}{3} =x + \dfrac{40}{9} + \dfrac{116}{15} }}$

Now, take the LCM in RHS and performing addition.

$\longrightarrow \sf{\quad { \dfrac{109}{3} =x + \dfrac{200 + 348}{45} }}$

Performing addition in the numerator of the fraction in RHS.

$\longrightarrow \sf{\quad { \dfrac{109}{3} =x + \dfrac{548}{45} }}$

Now, transposing 548/45 from RHS to LHS. Its sign will get changed.

$\longrightarrow \sf{\quad { \dfrac{109}{3} - \dfrac{548}{45} =x }}$

Taking the LCM in LHS and simplifying further.

$\longrightarrow \sf{\quad { \dfrac{1635 - 548}{45} =x }}$

Performing subtraction in the numerator of the fraction in LHS.

$\longrightarrow \sf{\quad { \dfrac{1087}{45} =x }}$

Now, converting the simple fraction into mix fraction.

$\longrightarrow \quad\underline{\boxed { \pmb{\frak{ 24}}\dfrac{\pmb{\frak{7}}}{\pmb{\frak{45 }}} \; \pmb{\frak{kg }}= \pmb{\frak{x}}}}$

Therefore, the weight of oranges is 24 ⁷/₄₅ kg.