Question 1098807: a stack of 20 coins contains only nickels and quarters and has a total value of $4 how many of each coin are in the stack Found 2 solutions by greenestamps, MathTherapy:Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website! First I'll show a solution using the standard algebraic method found in most textbooks, at least in the US. Then I'll show you an alternative method which I think is much faster and easier.
By algebra...:
let q = number of quarters
let n = number of nickels
then (1) (the total number of coins is 20)
and (2) (the total value of the coins, in cents, is 400)
Now solve the pair of equations
(3) (equation (1), multiplied by 5)
(4) (equation (2) minus equation (3))
There are 15 quarters and 5 nickels.
Using the method of alligation....
(1) If all 20 coins were quarters, the total value would be $5; if all were nickels, the total value would be $1.
(2) The actual total value, $4, is three-fourths of the way from $1 to $5.
(3) Therefore, 3/4 of the coins must be quarters; 3/4 of 20 is 15.
There are 15 quarters and 5 nickels. Answer by MathTherapy(10553) (Show Source): You can put this solution on YOUR website!
a stack of 20 coins contains only nickels and quarters and has a total value of $4 how many of each coin are in the stack
Let the number of nickels be N
Then number of quarters = 20 - N
We then get: .05N + .25(20 - N) = 4
.05N + 5 - .25N = 4
.05N - .25N = 4 - 5
- .2N = - 1
N, or number of nickels =
Number of quarters: