Yasmin has 18 coins in her pocket. She has nickels and dimes that total $1.20 how many nickels and how many dimes does she have
Let's assume Yasmin has x nickels and y dimes.
According to the problem, the total number of coins Yasmin has is 18. This can be written as an equation: x + y = 18.
The total value of all the nickels is given as the number of nickels multiplied by 0.05 (since a nickel is $0.05). So, the total value of the nickels is 0.05x.
Similarly, the total value of all the dimes is given as the number of dimes multiplied by 0.10 (since a dime is $0.10). So, the total value of the dimes is 0.10y.
According to the problem, the total value of all the coins (nickels + dimes) is $1.20. This can be written as another equation: 0.05x + 0.10y = 1.20.
We can solve these two equations simultaneously to find the values of x and y.
Multiplying the first equation by 0.05, we get: 0.05x + 0.05y = 0.90.
Subtracting this equation from the second equation: (0.05x + 0.10y) - (0.05x + 0.05y) = 1.20 - 0.90.
This simplifies to: 0.05y = 0.30.
Dividing both sides of the equation by 0.05, we get: y = 6.
Substituting this value of y into the first equation, we get: x + 6 = 18.
Subtracting 6 from both sides of the equation, we get: x = 12.
Therefore, Yasmin has 12 nickels and 6 dimes.
To find out how many nickels and dimes Yasmin has, we can set up a system of equations based on the information given.
Let's assume the number of nickels is represented by 'n' and the number of dimes is represented by 'd'.
1. We know that Yasmin has a total of 18 coins, so we can write the first equation:
n + d = 18
2. We also know that the value of the nickels and dimes combined is $1.20, which can be written as:
0.05n + 0.10d = 1.20
Now we can solve this system of equations to find the values of 'n' and 'd'.
We can start by multiplying the first equation by 0.05 to make the coefficients of 'n' the same:
0.05n + 0.05d = 0.05*18
This simplifies to:
0.05n + 0.05d = 0.90
Now we can subtract this new equation from the second equation to eliminate 'n':
(0.05n + 0.10d) - (0.05n + 0.05d) = 1.20 - 0.90
Simplifying further, we get:
0.05d = 0.30
Dividing both sides of the equation by 0.05, we find:
d = 0.30 / 0.05
Therefore, d = 6.
Now, substitute this value of d back into the first equation:
n + 6 = 18
Subtracting 6 from both sides, we get:
n = 18 - 6
Therefore, n = 12.
So, Yasmin has 12 nickels and 6 dimes.