URGENT
a coin bank contains dimes and quarters. the number of quarters is five less than four times the number of times. the total amount in the bank is $6.45. find the number of dimes in the bank.
Number of dimes ---- x
number of quarters --- 4x - 5
equation dealing with value
10x + 25(4x - 5) = 645
solve for x
Why did the dime go to therapy? It couldn't make cents of its identity crisis!
Alright, let's solve this money puzzle together. Let's say the number of dimes in the bank is represented by 'd' and the number of quarters is represented by 'q'. According to the problem, we have two pieces of information:
1. The number of quarters is five less than four times the number of dimes: q = 4d - 5
2. The total amount in the bank is $6.45. Since each dime is worth $0.10 and each quarter is worth $0.25, we can represent this information as the equation: 0.10d + 0.25q = 6.45
Now, let's substitute the value of q from the first equation into the second equation:
0.10d + 0.25(4d - 5) = 6.45
0.10d + 1.00d - 1.25 = 6.45
1.10d = 7.70
d = 7.70 / 1.10
d ≈ 7
So, there are approximately 7 dimes in the bank.
To solve this problem, we need to set up a system of equations using the given information.
Let's define the variables:
Let 'd' be the number of dimes in the bank.
Let 'q' be the number of quarters in the bank.
From the problem statement, we can translate the given information into equations:
1) "The number of quarters is five less than four times the number of dimes."
This can be written as: q = 4d - 5.
2) "The total amount in the bank is $6.45."
The value of each dime is $0.10, and the value of each quarter is $0.25. So the total value can be expressed as: 0.10d + 0.25q = 6.45.
Now we have a system of two equations:
q = 4d - 5
0.10d + 0.25q = 6.45.
To find the number of dimes in the bank, we need to solve this system of equations.
Step 1: Substitute the value of q from equation 1 into equation 2:
0.10d + 0.25(4d - 5) = 6.45.
Step 2: Simplify and solve for d:
0.10d + (1.00d - 1.25) = 6.45
0.10d + 1.00d - 1.25 = 6.45
1.10d - 1.25 = 6.45.
Step 3: Add 1.25 to both sides of the equation:
1.10d = 6.45 + 1.25
1.10d = 7.70.
Step 4: Divide both sides of the equation by 1.10:
d = 7.70 / 1.10
d ≈ 7.
Therefore, there are approximately 7 dimes in the bank.