Question

A bag contains 3 1/5 kg of Apples,6 1/2 kg of oranges, 7 3/10 kg of grapes,and some mangoes.If the total weight of the fruits is 25 1/10 kg,find the weight of the mangoes in the bag.

Answer 1

Given:

A bag contains:

Apples → $3\frac{1}{5} \:kg$ = $\frac{16}{5}\:kg$

Oranges → $6\frac{1}{2} \:kg$ = $\frac{13}{2} \:kg$

Grapes → $7\frac{3}{10} \:kg$ = $\frac{73}{10}\:kg$

Total weight of the fruits = $25\frac{1}{10}\:kg$ = $\frac{251}{10}$ $\:kg$

To find:

The weight of the mangoes in the bag.

Solution:

Let "x" kg be the weight of the mangoes in the bag.

According to the question, we can form an equation as,

[Weight of apples] + [Weight of oranges] + [Weight of grapes] + [Weight of mangoes] = Total weight of fruits in the bag

⇒ $\frac{16}{5}\: +\: \frac{13}{2} \:+\: \frac{73}{10}\: +\: x \:=\:\frac{251}{10}$

⇒ $\frac{32\:+\:65\:+\:73}{10} \:+\:x\:=\:\frac{251}{10}$

⇒ $\frac{170}{10} \:+\:x\:=\:\frac{251}{10}$

⇒ $\frac{170\:+\:10x}{10} \:=\:\frac{251}{10}$

⇒ $170\:+\:10x\:=\:251$

⇒ $10x\:=\:251 - 170$

⇒ $10x = 81$

⇒ $x = \frac{81}{10}$

⇒ $\bold{x\:=\:8\frac{1}{10}\:kg}$

Thus, the weight of the mangoes in the bag is $\underline{8\frac{1}{10}\:kg}$.

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