Every day when Lisa returns from school, she puts her change from buying lunch into a jar on her dresser. This weekend she decided to count her savings.
She found that she had 72 coins, all nickels and dimes. The total amount was $4.95. How many coins of each type did she have?
Be sure to explain how you found your answer.
Please help explain to me
N = 72 - D
10D + 5N = 4.95
Substitute 72-D for N in the second equation.
10D + 5(72-D) = 4.95
Solve for D, then put value in the first equation to find N.
It's 27
To solve this problem, we can set up a system of equations.
Let's represent the number of nickels as "n" and the number of dimes as "d".
From the information given, we know that Lisa has a total of 72 coins, so we can write the equation:
n + d = 72 (equation 1)
We also know that the total value of the nickels and dimes is $4.95. Since each nickel is worth $0.05 and each dime is worth $0.10, we can write a second equation for the total value:
0.05n + 0.10d = 4.95 (equation 2)
Now, we can solve this system of equations.
First, let's solve equation 1 for n:
n = 72 - d
Now substitute this value of n into equation 2:
0.05(72 - d) + 0.10d = 4.95
Simplify the equation:
3.60 - 0.05d + 0.10d = 4.95
0.05d = 1.35
Divide both sides by 0.05:
d = 27
Now substitute this value of d into equation 1 to find n:
n + 27 = 72
n = 72 - 27
n = 45
Therefore, Lisa has 45 nickels and 27 dimes.
To find the solution to this problem, we can use a system of equations. Let's assign variables to the unknowns.
Let's say the number of nickels Lisa has is "n" and the number of dimes she has is "d".
Since we know that she has a total of 72 coins, we can create the first equation:
n + d = 72 (equation 1)
Now, let's consider the value of the coins. The value of a nickel is $0.05, and the value of a dime is $0.10. We are told that the total value of the coins is $4.95. We can create the second equation:
0.05n + 0.10d = 4.95 (equation 2)
Now we have a system of equations. To solve it, we can use the method of substitution or elimination. Let's use the method of substitution:
From equation 1, we can isolate n:
n = 72 - d
Now we substitute this value of n in equation 2:
0.05(72 - d) + 0.10d = 4.95
3.60 - 0.05d + 0.10d = 4.95
0.05d = 1.35
d = 27
Now we substitute this value of d back into equation 1 to find n:
n + 27 = 72
n = 72 - 27
n = 45
So, Lisa has 45 nickels and 27 dimes.