Yes, I have 18 points in her pocket. She has nickels and dimes that total dollar and $.20 how many nickels and dimes does she have write and solve a system of equation to find the answer
Let's solve this problem by writing a system of equations.
Let's represent the number of nickels as 'n' and the number of dimes as 'd'.
We know that the total number of coins is 18:
n + d = 18 ----(equation 1)
We also know that the total value of the coins is $0.20:
0.05n + 0.10d = 0.20 ----(equation 2)
To solve the system of equations, we can use the substitution or elimination method. Let's use the substitution method.
Solve equation 1 for n:
n = 18 - d
Substitute the value of n in equation 2:
0.05(18 - d) + 0.10d = 0.20
Distribute 0.05:
0.90 - 0.05d + 0.10d = 0.20
Combine like terms:
0.05d = 0.20 - 0.90
0.05d = -0.70
Divide by 0.05:
d = -0.70/0.05
d = -14
Since the number of dimes cannot be negative, there is no solution to this system of equations. It seems that there might be an error in the problem description or the given information.
Let's assume the number of nickels is represented by 'n', and the number of dimes is represented by 'd'.
According to the given information, we know that the value of the nickels in cents is 5n and the value of the dimes in cents is 10d.
The total value of the coins is $0.20, which is equivalent to 20 cents. Therefore, we can write the equation:
5n + 10d = 20 (equation 1)
We also know that the total number of coins is 18. So we can write another equation:
n + d = 18 (equation 2)
Now, we have a system of equations:
5n + 10d = 20 (equation 1)
n + d = 18 (equation 2)
To solve this system of equations, we can use the substitution or elimination method.
Let's use the substitution method. We can rearrange equation 2 to express n in terms of d:
n = 18 - d
Now substitute this value of n into equation 1:
5(18 - d) + 10d = 20
Simplifying the equation:
90 - 5d + 10d = 20
90 + 5d = 20
5d = 20 - 90
5d = -70
d = -70/5
d = -14
Since the number of coins cannot be negative, this value of 'd' is not valid. It seems there is an error in the initial information or the problem itself. Please double-check the values provided.