Thomas and Siti had cookies in the ratio 3 : 7. After Thomas bought another 42 cookies and Siti ate 18 cookies of her own, they had an equal number of cookies left. How many cookies did Siti have at first? Ans: ___

1. Set up the initial ratio in terms of units

Let Thomas's initial cookies be $3u$ and Siti's initial cookies be $7u$.

2. Form an equation based on the final equal amounts

Thomas's final cookies = $3u + 42$
Siti's final cookies = $7u - 18$
Since they had an equal number of cookies left:
$3u + 42 = 7u - 18$

3. Solve for 1 unit ($u$)

$7u - 3u = 42 + 18$
$4u = 60$
$u = 15$

4. Calculate Siti's initial number of cookies

Siti's initial cookies = $7u = 7 \times 15 = 105$