Answer:
-39
Explanation:
To find the number of quarters in the bank, let's break down the problem step by step.
1. Let's assume the number of dimes in the bank is "x".
2. Since there are 7 more nickels than dimes, the number of nickels would be "x + 7".
3. The total number of coins in the bank is given as 140. So we can write an equation: x + (x + 7) + Number of quarters = 140.
Now, let's calculate the value of each coin:
1. The value of a nickel is $0.05.
2. The value of a dime is $0.10.
3. The value of a quarter is $0.25.
To determine the value of the coins, we can set up another equation: 0.05 * (x + 7) + 0.10 * x + 0.25 * Number of quarters = $3.60.
Now, we have two equations:
1. x + (x + 7) + Number of quarters = 140.
2. 0.05 * (x + 7) + 0.10 * x + 0.25 * Number of quarters = $3.60.
Solving these equations simultaneously will give us the number of quarters.
Let's solve the equations:
1. Combine like terms: 2x + 7 + Number of quarters = 140.
2. Simplify further: 2x + Number of quarters = 133.
Now, let's substitute the value of x from the first equation into the second equation: 0.05 * (x + 7) + 0.10 * x + 0.25 * Number of quarters = $3.60. 0.05 * (x + 7) + 0.10 * x + 0.25 * (133 - 2x) = $3.60.
Simplify further: 0.05x + 0.35 + 0.10x + 33.25 - 0.50x = $3.60.
Combine like terms: -0.35x + 33.60 = $3.60.
Subtract 33.60 from both sides: -0.35x = -$30.
Divide both sides by -0.35: x = 86.
Now that we have the value of x, we can substitute it back into the first equation to find the number of quarters: 86 + (86 + 7) + Number of quarters = 140.
Combine like terms: 179 + Number of quarters = 140. Subtract 179 from both sides: Number of quarters = -39.
Since it doesn't make sense to have a negative number of quarters, it seems there was an error in the problem.