#### Question

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

Question

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

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