Hello, I need help with these math problems and I don't know how to work them out. under this I will give the questions I need help with and I will also put the answers at the bottom so you can check your answers. I've been lost with the section for a while so any help is good. Algebra 2- word problems with 3 variables

1. Barbra has 19 coins consisting of nickels, dimes, quarters, which are worth a total of $2.35 in her purse. The number of dimes is three less than the sum of the number of nickels and quarters. how many of each type does she have?

2. When three large diamonds are weighed in pairs, the masses of the pairs are found to be 6 carats, 10 carats, and 12 carats. find the mass of each diamond.

3. The high school theater sold $10 patron tickets, $5 sponsor tickets, and $2.50 donor tickets to raise money for the play. The number of donor tickets was 24 more than the number of sponsors and patron tickets combined. There were 326 sold, and the receipts totaled $1432.50. How many of each type were sold?

The answers to the questions are
1.(6,8,5)
2.(2,4,8)
3.(48,103,175)

Your help would be greatly appreciated. I just need to know step by step how you solve and how you go that so I can learn what I'm doing . Thank you so much.