Question

Prudence is one and a half times older than Patience, and Patience is one and a
half times older than Charity. How old are Prudence, Patience and Charity if their
combined ages total 133?
Charity 28, Patience 42, Prudence 63
O Charity 42, Patience 63, Prudence 28
Charity 28, Patience 63, Prudence 42
O none of the above
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Answer 1

Given: Prudence is one and a half times older than Patience, and Patience is one and a  half times older than Charity. Their combined ages total 133.

To find: Ages of Prudence, Patience and Charity.

Explanation:

Option A: Charity 28, Patience 42, Prudence 63

Let the age of charity be: a years

Then, the age of Patience (1.5 times of age of Charity) = 1.5a

The age of Prudence = 1.5 times of age of Patience

                                    = 2.25a

We know:

age of Prudence + Patience+ Charity = 133

$2.25a + 1.5 a + a= 133\\4.75 a= 133\\a=\frac{133}{4} \\a= 28$

Age of Charity: 28 years

Age of Patience: $1.5\times 28=42$ years

Age of Prudence:$2.25 \times 28= 63 years$