molly has 14 coins in her pocket. She has nickels and dimes that total $1.10 How many nickels and how many dimes does she have?
Let's use a system of equations to solve this problem:
n = number of nickels
d = number of dimes
From the problem, we know that:
n + d = 14 (since Molly has 14 coins in total)
0.05n + 0.10d = 1.10 (since the value of all her coins is $1.10)
Now we can use the first equation to solve for one of the variables in terms of the other:
n = 14 - d
Substituting this into the second equation, we get:
0.05(14 - d) + 0.10d = 1.10
Expanding and simplifying:
0.70 - 0.05d + 0.10d = 1.10
0.05d = 0.40
d = 8
So Molly has 8 dimes. We can substitute this back into the first equation to find the number of nickels:
n + 8 = 14
n = 6
Therefore, Molly has 6 nickels and 8 dimes.
To solve this, we can set up a system of equations.
Let's assume "n" represents the number of nickels and "d" represents the number of dimes.
From the given information, we know that:
1. The total number of coins is 14: n + d = 14
2. The value of the coins is $1.10: 0.05n + 0.10d = 1.10
We can simplify the second equation by multiplying both sides by 100 to eliminate decimals:
5n + 10d = 110
Now, we have a system of equations:
n + d = 14
5n + 10d = 110
From the first equation, we can solve for n in terms of d:
n = 14 - d
Substituting this into the second equation, we get:
5(14 - d) + 10d = 110
70 - 5d + 10d = 110
5d = 40
d = 8
Substituting the value of d back into the first equation, we find:
n + 8 = 14
n = 6
Therefore, Molly has 6 nickels and 8 dimes.
To find out how many nickels and dimes Molly has, we can use algebraic equations.
Let's assume that Molly has x nickels and y dimes.
1. The total number of coins Molly has is given as 14. So, we can write the equation:
x + y = 14.
2. The total value of the nickels and dimes is given as $1.10, which is equal to 110 cents. Since a nickel is worth 5 cents and a dime is worth 10 cents, we can write the equation for the total value as:
5x + 10y = 110.
To find the values of x and y, we can solve this system of equations.
First, we can solve the first equation (x + y = 14) for x:
x = 14 - y.
Now, substitute this value into the second equation:
5(14 - y) + 10y = 110.
Simplifying the equation:
70 - 5y + 10y = 110,
5y = 40,
y = 8.
So, Molly has 8 dimes.
Substitute the value of y into the first equation to find x:
x + 8 = 14,
x = 14 - 8,
x = 6.
Therefore, Molly has 6 nickels.
In conclusion, Molly has 6 nickels and 8 dimes.