A person has 20 coins, all nickels and dimes, worth $1.65. How many nickels are there?

Question

sciencyguy · Answer

You have two "facts," and two unknowns. 
Your two facts are: total number of coins is 20; and total value of coins is $1.65.
Actually, you have two more facts..you know that dimes are worth $0.10 and nickels worth $0.05.
Can you take the facts you know, and put them in two independent equations.
If "dimes" is the number of dimes and "nickels" the number of nickels, then the total number of coins is simply the sum of the dimes and nickels:
$$dimes + nickels = total = 20$$
Rearranging, the equation is:
$$dimes = 20 - nickels.$$
Now, given what you know about how much value one dime has and how much value one nickel has, can you write an equation that expresses the total value ($1.65) in terms of the number of nickels and dimes?
Once you do that, you will replace every "dimes" that appears in your new equation with the result from your first equation. Then the only unknown appearing in the equation will be "nickels" and you can answer the question.

anonymous · Answer

& the answer is......?

sciencyguy · Answer

Can you write the second equation? What's the total value expressed as a number of dimes and a number of nickels?  Don't worry about rushing to the answer...