Phil has 20 coins, nickels,dimes, and quarters, totaling $2.30. If he has twice as many nickels as quarters, how many quarters does Phil have?
Putting each piece of information into symbols, we have
n+d+q = 20
n = 2q
5n+10d+25q = 230
So, what do you get?
To solve this problem, we need to set up a system of equations based on the information given.
Let's say Phil has x quarters and 2x nickels. We can also represent the number of dimes as (20 - x - 2x), since he has a total of 20 coins.
The value of the quarters is 25 cents each, so the value of all the quarters is 25x cents.
The value of the nickels is 5 cents each, so the value of all the nickels is 5 * 2x = 10x cents.
The value of the dimes is 10 cents each, so the value of all the dimes is 10 * (20 - x - 2x) = 200 - 30x cents.
Now, we can set up the equation based on the total value of the coins: 25x + 10x + (200 - 30x) = 230 cents.
Simplifying the equation, we get: 25x + 10x + 200 - 30x = 230
Combining like terms, we get: 5x + 200 - 30x = 230
Simplifying further, we get: -25x + 200 = 230
Subtracting 200 from both sides of the equation, we get: -25x = 30
Dividing both sides of the equation by -25, we get: x = -30 / -25
Simplifying, we get: x = 6
Therefore, Phil has 6 quarters.