The ratio of the number of sweets Rachel had to the number of sweets Euodia had was 2 : 3 at first. After Rachel bought 8 more sweets, the ratio of the number of sweets Rachel had to the number of sweets Euodia had became 5 : 6. How many sweets did Euodia have? Ans: ___

1. Identify the unchanged quantity and make its units equal in both ratios

Euodia's number of sweets remains unchanged.
Initial ratio of Rachel to Euodia = $2 : 3$
Final ratio of Rachel to Euodia = $5 : 6$
To make Euodia's units the same, multiply the initial ratio by $2$:
Initial ratio = $4 : 6$

2. Find the value of 1 unit based on the change in Rachel's sweets

Increase in Rachel's units = $5 - 4 = 1$ unit
$1 \text{ unit} = 8 \text{ sweets}$

3. Calculate the number of sweets Euodia had

Euodia's units = $6$
Number of sweets Euodia had = $6 \times 8 = 48$