In a change jar, Tom has nickels and dimes. The number of nickels is two times the number of dimes and the total amount of money in the jar is $1.20. How many dimes are in the jar?
Nickels are worth .5 and dimes are worth .10. You could set up x as the number of nickelse and y as the number of dimes. So you could set up your first equation as:
.5x+.10y=1.20
Second equation: 2x=y now you could just plug in 2x for y in the first equation and solve your equation
number of dimes --- x
number of nickels --- 2x
10x + 5(2x) = 120
20x = 120
x = 6
So 6 dimes and 12 nickels
Let's assume the number of dimes in the jar is D.
According to the given information, the number of nickels is two times the number of dimes. So, the number of nickels is 2D.
Now, let's calculate the value of the dimes. Since each dime is worth 10 cents, the total value of the dimes in the jar would be 10D cents.
Similarly, the value of the nickels can be calculated. Since each nickel is worth 5 cents, the total value of the nickels in the jar would be 5 * (2D) cents, which simplifies to 10D cents.
Now, we know that the total amount of money in the jar is $1.20. Converting this to cents, it is equal to 120 cents.
So, the equation we can set up is:
10D (value of dimes) + 10D (value of nickels) = 120 (total value of money in cents)
Combining like terms, we have:
20D = 120
Dividing both sides by 20, we can solve for D:
D = 120 / 20
D = 6
Therefore, there are 6 dimes in the jar.
To solve this problem, we can set up a system of equations based on the given information. Let's assign variables to the unknown quantities.
Let:
N = Number of nickels
D = Number of dimes
From the problem statement, we can get two equations:
1) The number of nickels is two times the number of dimes:
N = 2D
2) The total amount of money in the jar is $1.20:
0.05N + 0.10D = 1.20
Now we can substitute the value of N from equation 1) into equation 2):
0.05(2D) + 0.10D = 1.20
0.10D + 0.10D = 1.20
0.20D = 1.20
D = 1.20 / 0.20
D = 6
Therefore, there are 6 dimes in the jar.