Winborne has 35 coins consisting of dimes and nickels. If the value of his coins is $3.30 then how many of each type does he have?
Please help to check on correct answer
my answer is 31 dimes and 3 nickels
Looks like you might have a typo there.
Total number of coins = 35
Number of dimes = x
Number of nickels nickels = 35 - x
Value of 1 dime = 0.10
Value of 1 nickel = 0.05
0.10x + 0.05(35 - x) = 3.30
0.10x + 1.75 - .05x = 3.30
0.05x = 1.55
x = 31 dimes
35 - 31 = 4 nickels
Oh no. Sorry about the extra "nickels"!
To solve this problem, we can set up a system of equations.
Let's assume Winborne has x dimes and y nickels.
From the given information, we know that Winborne has a total of 35 coins:
x + y = 35 (Equation 1)
We also know that the value of Winborne's coins is $3.30:
0.10x + 0.05y = 3.30 (Equation 2)
Now we can solve these equations simultaneously.
To do that, we can multiply Equation 1 by 0.05 to make the coefficients of y the same in both equations:
0.05x + 0.05y = 1.75 (Equation 3)
We can subtract Equation 3 from Equation 2 to eliminate y:
0.10x - 0.05x + 0.05y - 0.05y = 3.30 - 1.75
0.05x = 1.55
x = 1.55 / 0.05
x = 31
Now we can substitute the value of x into Equation 1 to find y:
31 + y = 35
y = 35 - 31
y = 4
Therefore, Winborne has 31 dimes and 4 nickels, not 31 dimes and 3 nickels as you mentioned.
To solve this problem, we can set up a system of equations. Let's denote the number of dimes as "d" and the number of nickels as "n".
We know that there are 35 coins in total, so we can write the first equation as:
d + n = 35 (Equation 1)
We also know that the value of the coins is $3.30. Since dimes are worth 10 cents and nickels are worth 5 cents, we can write the second equation as:
10d + 5n = 330 (Equation 2)
To solve this system of equations, we can use substitution or elimination. Let's use substitution.
From Equation 1, we can express "n" in terms of "d" as:
n = 35 - d
Substitute this expression for "n" in Equation 2:
10d + 5(35 - d) = 330
Simplify the equation:
10d + 175 - 5d = 330
5d = 155
d = 31
Now substitute the value of "d" into Equation 1 to find "n":
31 + n = 35
n = 35 - 31
n = 4
So, the correct answer is 31 dimes and 4 nickels, not 31 dimes and 3 nickels.