You have a piggy bank containing a total of 85 coins in dimes and quarters. If the piggy bank contain $14.50, how many dimes are there in the piggy bank?
Interest=principal multiply Rate multiply 1, or interest=principal multiply rate.
d = number of dimes
.10d = value of dimes
85 - d = number of quarters
.25(85 - d) = value of quarters
0.10d + .25(85 - d) = 14.50
Solve for d, number of dimes
85 - d = number of quarters
To solve this problem, we can use a system of equations.
Let's say the number of dimes in the piggy bank is "d" and the number of quarters is "q".
We know that the total number of coins is 85, so we can write the equation:
d + q = 85.....(Equation 1)
We also know that the total value of the coins in the piggy bank is $14.50. Since each dime is worth $0.10 and each quarter is worth $0.25, we can write another equation based on the value of the coins:
0.10d + 0.25q = 14.50.....(Equation 2)
Now we have a system of equations to solve for "d" and "q".
To solve the system of equations, we can use substitution or elimination method. In this case, let's use the elimination method.
Multiply Equation 1 by 0.10 to make the coefficients of "d" in both equations the same:
0.10d + 0.10q = 8.50.....(Equation 3)
Now subtract Equation 3 from Equation 2:
0.10d + 0.25q - (0.10d + 0.10q) = 14.50 - 8.50
0.10q - 0.10q + 0.25q - 0.10q = 6
0.15q = 6
q = 6 / 0.15
q = 40
Substitute the value of "q" into Equation 1 to solve for "d":
d + 40 = 85
d = 85 - 40
d = 45
Therefore, there are 45 dimes in the piggy bank.