A box contains 140 dimes and nickels.
The total value is $11.15. How many dimes and nickels are there?
Need the help finding the formula.
Let d = # dimes and
n = # nickels.
Set up two equations from the problem.
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d + n = 140
0.10d + 0.05n = 11.15
Solve for d and n.
Post your work if you get stuck. I suggest you multiply equation 1 by -0.05 and add it to equation 2, then solve.
To solve this problem, we can use a combination of algebra and basic arithmetic.
Let's denote the number of dimes as "d" and the number of nickels as "n".
From the given information, we know that:
1. The total number of dimes and nickels is 140: d + n = 140.
2. The total value of the dimes and nickels is $11.15:
0.10d + 0.05n = 11.15.
Now we have a system of two equations with two variables:
d + n = 140
0.10d + 0.05n = 11.15.
This system can be solved using substitution or elimination. We will use elimination.
To eliminate the decimal, we can multiply both sides of the second equation by 100:
10d + 5n = 1115.
Now we can multiply the first equation by -5 to make the coefficients of "n" in both equations equal:
-5(d + n) = -5(140)
-5d - 5n = -700.
Next, add the two equations together:
(10d + 5n) + (-5d - 5n) = 1115 + (-700)
5d = 415.
Divide both sides of the equation by 5:
5d/5 = 415/5
d = 83.
Now substitute the value of "d" back into the first equation to find the value of "n":
83 + n = 140
n = 140 - 83
n = 57.
So there are 83 dimes and 57 nickels in the box.
To solve this problem, we can set up a system of equations to represent the given information. Let's let 'd' represent the number of dimes and 'n' represent the number of nickels.
The first equation is based on the number of coins in the box: d + n = 140 (since there are 140 dimes and nickels in total)
The second equation is based on the total value of the coins: 0.1d + 0.05n = 11.15 (since a dime is worth $0.10 and a nickel is worth $0.05)
So, the system of equations becomes:
d + n = 140
0.1d + 0.05n = 11.15
Next, we can use the method of substitution or elimination to solve the system of equations. Let's use the substitution method for this problem.
From the first equation, we can express 'n' in terms of 'd': n = 140 - d
Now we substitute this expression for 'n' in the second equation:
0.1d + 0.05(140 - d) = 11.15
Simplifying the equation:
0.1d + 7 - 0.05d = 11.15
0.05d = 11.15 - 7
0.05d = 4.15
Now, we can solve for 'd' by dividing both sides of the equation by 0.05:
d = 4.15 / 0.05
d = 83
So, there are 83 dimes in the box. To find the number of nickels, we can substitute this value of 'd' back into the first equation:
83 + n = 140
n = 140 - 83
n = 57
Therefore, there are 83 dimes and 57 nickels in the box.