phil has 50 nickles and dimes worth $4.15. how many dimes does he have?
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\(10x+5(50-x)=415\) if the number of dimes is \(x\)
Laura. . . it looks like the answer of "daSVgrouch" is incorrect. Here is the correct answer for you:
Let n = number of nickels
Let d = number of dimes
The total of our individual nickels and dimes, is 50. So:
n + d = 50
Also, we know that our total in money is 415 cents.
5n + 10d = 415
So, we have 2 equations.
n + d = 50 (equation 1)
5n + 10d = 415 (equation 2)
We can use addition, subtraction, or substitution.
-5n + -5d = -250 (equation 1 multiplied through by "negative 5")
5n + 10d = 415
Now add the two equations. . .
0n + 5d = 165
Simplify. . .
5d = 165
d = 33
If d = 33 and we have 50 total coins, then n = 17.
He has 33 dimes.
I used to teach mathematics in high school.
dimes are worth ten cents each, and if there are a total of 50 coins and \(x\) dimes then there are \(50-x\) nickles worth 5 cents each.
you have a total of 415 cents so set
\[10x+5(50-x)=415\]solve for \(x\)