Chelsea had 23 nickels and dimes worth $1.60
5 n + 10 d = 160
n + d = 23
so
d = (23-n)
5 n + 10 ( 23 - n) = 160
5 n - 10 n = 160 - 230
- 5 n = -70
n = 14
d = 9
Well, that sounds like Chelsea had quite the change in her pocket! With 23 nickels and dimes, she must have been jiggling all the way. And to have a total of $1.60? That's some serious coinage! It's amazing what you can find at the bottom of a couch cushion or hidden in those sneaky pockets. Good on Chelsea for keeping track of her treasure!
To solve this problem, let's set up a system of equations.
Let's assume Chelsea has x nickels and y dimes.
1) The total number of coins Chelsea has is 23:
x + y = 23
2) The total value of the coins is $1.60:
0.05x + 0.10y = 1.60
Now, we can solve this system of equations using any method, such as substitution or elimination.
Let's solve by substitution method:
From equation 1, we have:
x = 23 - y
Substituting this value into equation 2:
0.05(23 - y) + 0.10y = 1.60
Expanding the equation and combining like terms:
1.15 - 0.05y + 0.10y = 1.60
Combining like terms:
0.05y = 0.45
Dividing both sides by 0.05:
y = 9
Now, substitute the value of y back into equation 1:
x + 9 = 23
Subtracting 9 from both sides:
x = 14
Therefore, Chelsea has 14 nickels and 9 dimes.
To determine how many nickels and dimes Chelsea has, we can set up a system of equations.
Let's assign variables to represent the number of nickels and dimes. Let n represent the number of nickels and d represent the number of dimes.
We are given two pieces of information. Firstly, we know that Chelsea has a total of 23 nickels and dimes, so we can write the equation:
n + d = 23
Secondly, we know that the combined value of the nickels and dimes is $1.60.
The value of a nickel is $0.05, so the value of n nickels is 0.05n.
Similarly, the value of a dime is $0.10, so the value of d dimes is 0.10d.
Therefore, we can write the second equation:
0.05n + 0.10d = 1.60
Now we have a system of equations:
n + d = 23
0.05n + 0.10d = 1.60
To solve this system of equations, there are multiple methods, such as substitution or elimination. Let's use the elimination method to solve this system.
To eliminate the decimal in the second equation, we can multiply both sides of the equation by 100:
100(0.05n + 0.10d) = 100(1.60)
Simplifying, we get:
5n + 10d = 160
Now we have a new system of equations:
n + d = 23
5n + 10d = 160
To eliminate the d variable, we can multiply the first equation by -10 and add it to the second equation:
-10(n + d) + (5n + 10d) = -10(23) + 160
Simplifying, we get:
-5n = -70
Dividing both sides by -5, we find:
n = 14
Now that we know the value of n, we can substitute it back into the first equation to find the value of d:
14 + d = 23
Subtracting 14 from both sides, we find:
d = 9
Therefore, Chelsea has 14 nickels and 9 dimes.