Apiggy bank contains 36 coins that consists of dimes and quarters totaling $5.85 how many quarters are in the piggy bank in your final answer include all nessescary calculations !

The main idea here is to "translate" the words into maths. 
First we need to identify the unknowns and label these. 

We need to know the number if dimes and the number of quarters. So lets say
x: number of dimes
y: number of quarters

Now lets write equations from the written problem. 
We know that there are 36 coind total, thus: 
x + y = 36
We also know that the coins total 5.85 dollars, but it is better to count in cents, that is 585 cents. 
x are the number of dimes, their value is x*10
y are quarters with value of y*25
thus: 
10x+25y=585

We have two equations and two unknowns now, that needs to be solved to get the answer. 

x + y = 36
10x+25y=585