Fred has 3 times as many dimes as quarters. How many dimes does he have if the value of all the coins is $3.85?
It's easier to find the number of quarters:
10*3q + 25q = 385
55q = 385
q = 7
so, d=3q=21
Let's assume that the number of quarters Fred has is x.
Since Fred has 3 times as many dimes as quarters, he would have 3x dimes.
The value of a quarter is $0.25, so the total value of all the quarters Fred has would be 0.25x.
The value of a dime is $0.10, so the total value of all the dimes Fred has would be 0.10 * (3x) = 0.30x.
The total value of all the coins is $3.85, so we can set up the following equation:
0.25x + 0.30x = 3.85
Combining like terms, we have:
0.55x = 3.85
Dividing both sides by 0.55, we find:
x = 3.85 / 0.55
x ≈ 7
Therefore, Fred has 7 quarters.
Since Fred has 3 times as many dimes as quarters, he would have 3 * 7 = 21 dimes.
So, Fred has 21 dimes.
To solve this problem, let's break it down step by step:
Step 1: Assign variables
Let's assign variables to the unknowns in the problem:
Let "q" represent the number of quarters Fred has.
Let "d" represent the number of dimes Fred has.
Step 2: Set up equations based on the given information
From the problem statement, we know that Fred has 3 times as many dimes as quarters, which can be written as:
d = 3q (Equation 1)
We also know that the value of all the coins is $3.85. The value of a quarter is $0.25, and the value of a dime is $0.10. So, we can set up another equation based on the values of the coins:
0.25q + 0.10d = 3.85 (Equation 2)
Step 3: Solve the equations
Now, we need to solve the system of equations (Equation 1 and Equation 2) to find the values of "q" and "d".
Substitute the value of "d" from Equation 1 into Equation 2:
0.25q + 0.10(3q) = 3.85
0.25q + 0.30q = 3.85
0.55q = 3.85
q = 3.85 / 0.55
q ≈ 7
Now substitute the value of "q" back into Equation 1 to find the value of "d":
d = 3q
d = 3(7)
d = 21
Step 4: Answer the question
Therefore, Fred has 21 dimes.