Mukul has $1.60 in nickels, dimes, and quarters. He has nine more dimes than quarters and six more nickels than quarters. How many of each coin are in his pocket.
do this one the same way as the previous coin problem. Add up the values and use the information about how many coins there are.
Let's break down the problem step-by-step to solve it:
Step 1: Let's assume the number of quarters Mukul has as "x".
Step 2: Since Mukul has nine more dimes than quarters, the number of dimes he has would be "x + 9".
Step 3: Similarly, since Mukul has six more nickels than quarters, the number of nickels he has is "x + 6".
Step 4: Now, let's calculate the total value Mukul has in dollars. The value of a quarter is $0.25, the value of a dime is $0.10, and the value of a nickel is $0.05. Thus, the total value is:
0.25(x) + 0.10(x + 9) + 0.05(x + 6) = $1.60
Step 5: Simplifying the equation, we have:
0.25x + 0.10x + 0.90 + 0.05x + 0.30 = $1.60
0.40x + 1.20 = $1.60
Step 6: Subtracting $1.20 from both sides, we get:
0.40x = $1.60 - $1.20
0.40x = $0.40
Step 7: Dividing both sides of the equation by 0.40, we have:
x = $0.40 / 0.40
x = 1
Step 8: So, Mukul has 1 quarter.
Step 9: Using the values of x, we can find the number of dimes and nickels Mukul has:
Number of dimes = x + 9 = 1 + 9 = 10
Number of nickels = x + 6 = 1 + 6 = 7
Step 10: Therefore, Mukul has 1 quarter, 10 dimes, and 7 nickels in his pocket.
To solve this problem, we can use a system of equations.
Let's represent the number of quarters as "q." Since Mukul has nine more dimes than quarters, the number of dimes will be represented as "q + 9." Similarly, since he has six more nickels than quarters, the number of nickels will be represented as "q + 6."
The value of a quarter is $0.25, the value of a dime is $0.10, and the value of a nickel is $0.05.
Now we can set up an equation to represent the total value of the coins:
0.25q + 0.10(q + 9) + 0.05(q + 6) = 1.60
Simplifying the equation:
0.25q + 0.10q + 0.90 + 0.05q + 0.30 = 1.60
0.40q + 1.20 = 1.60
0.40q = 1.60 - 1.20
0.40q = 0.40
q = 0.40 / 0.40
q = 1
We have found that there is 1 quarter in Mukul's pocket.
Substituting the value of q into the expressions for dimes and nickels:
Number of dimes = q + 9 = 1 + 9 = 10
Number of nickels = q + 6 = 1 + 6 = 7
Therefore, Mukul has 1 quarter, 10 dimes, and 7 nickels in his pocket.