Devi and Ali each spent the same amount of money. Devi had $\tfrac{1}{4}$ of his money left and Ali had had $\tfrac{3}{5}$ of his money left. What was the ratio of the amount of money Devi had at first to the amount of money Ali had at first? Ans: ___

1. Find the fraction of money spent by each person.

Fraction of money Devi spent = $1 - \frac{1}{4} = \frac{3}{4}$
Fraction of money Ali spent = $1 - \frac{3}{5} = \frac{2}{5}$

2. Equate the fractions of money spent and make their numerators the same.

Since they spent the same amount of money:
$\frac{3}{4}$ of Devi's money = $\frac{2}{5}$ of Ali's money
Make the numerators the same (LCM of 3 and 2 is 6):
$\frac{6}{8}$ of Devi's money = $\frac{6}{15}$ of Ali's money

3. Determine the ratio of their initial amounts.

From the denominators, Devi's total money is 8 units and Ali's total money is 15 units.
Ratio of Devi's money at first to Ali's money at first = $8 : 15$