Jeramie has a jar of nickels and dimes. There are 200 coins worth $14.00. How many of each type of coin are in the jar. :)
X Nickels.
(200-X) Dimes.
5x + 10(200-X) = 1400 Cents.
5x + 2000 - 10x = 1400
-5x = 1400 - 2000 = -600
X = 120 Nickels.
200-x = 200-120 = 80 Dimes.
Let's use variables to represent the number of nickels and dimes in the jar. Let's say the number of nickels is represented by 'x' and the number of dimes is represented by 'y'.
According to the given information, we can write two equations:
1. The total number of coins: x + y = 200.
2. The total value of the coins: (0.05 * x) + (0.10 * y) = 14.00.
To solve these equations, we can use the substitution method or the elimination method. Let's use the substitution method in this case.
From the first equation, express 'x' in terms of 'y':
x = 200 - y.
Now substitute this expression for 'x' into the second equation:
(0.05 * (200 - y)) + (0.10 * y) = 14.00.
Simplify the equation:
10 - 0.05y + 0.10y = 14.00.
0.05y = 4.00.
y = 4.00 / 0.05.
y = 80.
Now substitute the value of 'y' back into the first equation to find 'x':
x + 80 = 200,
x = 200 - 80,
x = 120.
So, there are 120 nickels and 80 dimes in the jar.
To solve this problem, we need to set up a system of equations using the given information. Let's say the number of nickels is represented by 'n' and the number of dimes is represented by 'd'.
From the first sentence, we know that the total number of coins in the jar is 200. So, we can set up our first equation as:
n + d = 200.
From the second sentence, we know that the total value of the coins is $14.00. Since there are 5 cents in a nickel and 10 cents in a dime, we can set up our second equation as:
5n + 10d = 1400. (converting dollars to cents)
Now we have a system of equations:
n + d = 200,
5n + 10d = 1400.
To solve this system, we can use a method called substitution or elimination. Let's use the substitution method.
From the first equation, we can solve for n: n = 200 - d.
Now we substitute this value for n in the second equation:
5(200 - d) + 10d = 1400.
Simplifying the equation, we get:
1000 - 5d + 10d = 1400,
5d = 400,
d = 80.
Now that we have the value of d (the number of dimes), we can substitute it back into either of the original equations to find n.
Using n + d = 200:
n + 80 = 200,
n = 200 - 80,
n = 120.
So, there are 120 nickels and 80 dimes in the jar.