Sure! Let's solve it step by step.
1. We know from the problem that Dulcina has 34 more pins than Eva does. This means that Dulcina's collection is Eva's collection plus 34 pins.
2. Together, Eva and Dulcina have a total of 82 pins. This means that if we add the number of pins in both collections, it should total 82.
3. If we represent the number of pins in Eva's collection as 'x', the above two steps could be represented in equation as: x + (x + 34) = 82.
4. Simplifying this equation gives us 2x + 34 = 82. To isolate the term with 'x', we subtract 34 from both sides of the equation, resulting in 2x = 48.
5. To find the value for 'x', which represents the number of pins in Eva's collection, we then divide both sides of the equation by 2, which gives us x = 24.
6. So, Eva has 24 pins in her collection.
7. Now, since Dulcina has 34 more pins than Eva, we add 34 to Eva's total to find the number of pins in Dulcina's collection. This gives us Dulcina's total as 24 + 34 = 58.
Therefore, Eva has 24 pins and Dulcina has 58 pins in their collections.