please help

17 quarters and 37 nickels

I have 54 coins in my pocket; some of them are quarters and the rest are nickels. In total, the coins are worth $6.10. How many of each coin do I have?

d+n=54

10d+5n=610

now solve simultaneously.  

I have 54 coins in my pocket; some of them are quarters and the rest are nickels. In total, the coins are worth $6.10. How many of each coin do I have? 

You have 54 coins.  If they were all nickels, you'd have 2.70 

2.70 is 3.40 short of 6.10 so you need to replace some of the nickels with quarters. 

Every time you replace a quarter with a nickel, you gain 0.20 

How many 0.20 gains do you need to increase your total by 3.40? 

3.40/0.20 = 17 so it takes 17 of those gains to make 3.40 so you have  17 quarters 

The remaining number of coins is 54 – 17 = 37 so you have                   37 nickels 

_• 

"Every time you replace a quarter with a nickel, you gain 0.20"

Darn it, I said it crossways.  I should have said every time you replace a nickel with a quarter. 

_π