If a quantity is divided in the ratio $$5 : 7$$, the larger part is $$84$$. Find the quantity.

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Uniteasy Admin · Accepted Answer

The larger part refers to the part of 7 in the ratio of the division.
The ratio of small part to the large part is given as $$5:7$$, or $$\dfrac{5}{7} $$
Then the ratio of the large part to the whole quantity is $$\dfrac{7}{5+7} = \dfrac{7}{12}  $$
Let the quantity be denoted as $$x$$. Since the larger part is $$84$$, then we have the following equation
$$\dfrac{7}{12}x=84 $$
Solve for $$x$$
$$x=144$$

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