A jar of change has 28 coins which is worth $2.60. If the jar only has nickels and dimes, how many of each type are in the jar?
X nickels.
(28-x) dimes.
5x + 10(28-x) = 260 cents.
X = ?.
not anonymous.
To figure out the number of nickels and dimes in the jar, we can set up a system of equations based on the given information.
Let's assume the number of nickels in the jar is 'n' and the number of dimes is 'd'.
From the given information, we can create two equations:
Equation 1: n + d = 28 (because there are a total of 28 coins)
Equation 2: 0.05n + 0.10d = 2.60 (because the value of nickels is $0.05 and the value of dimes is $0.10)
To solve this system of equations, we can use substitution, elimination, or another method of your choice.
Method 1: Substitution
Let's solve Equation 1 for n. Subtract d from both sides:
n = 28 - d
Now substitute this value of n into Equation 2:
0.05(28 - d) + 0.10d = 2.60
Now, solve for d:
1.40 - 0.05d + 0.10d = 2.60
0.05d = 2.60 - 1.40
0.05d = 1.20
Divide both sides by 0.05:
d = 1.20 / 0.05
d = 24
Now substitute this value of d back into Equation 1 to find n:
n + 24 = 28
n = 28 - 24
n = 4
Therefore, there are 4 nickels and 24 dimes in the jar.