The math question is "in a piggy bank there is a total of $15.75. If the ratio of dimes to quarters is 5:7, find the total amount in quarters.
My question is, what formula would I use to solve this?
10*5x + 25*7x = 1575
x = 7
. . .
To solve this problem, you can use a system of equations. Let's assign variables to the unknowns.
Let D represent the number of dimes,
and let Q represent the number of quarters.
1. Convert the given ratio of dimes to quarters to fractions:
The ratio of dimes to quarters is 5:7, which can be written as 5/7.
This means for every 5 dimes, there are 7 quarters.
2. Express the relationships between the variables in equations:
Since the value of each dime is $0.10 and each quarter is $0.25, we can create two equations based on the given information:
Equation 1: Dimes value equation
D * 0.10 = (5/7) * (D + Q) * 0.10
Equation 2: Quarters value equation
Q * 0.25 = (5/7) * (D + Q) * 0.25
3. Simplify the equations:
Equation 1: D * 0.10 = (5/7) * (D + Q) * 0.10
Simplify the equation to: D = (5/7) * (D + Q)
Equation 2: Q * 0.25 = (5/7) * (D + Q) * 0.25
Simplify the equation to: Q = (5/7) * (D + Q)
4. Substitute the value of D from equation 1 into equation 2:
Q = (5/7) * ([(5/7) * (D + Q)] + Q)
5. Solve the equation:
Simplify the equation: Q = (25/49) * (D + Q) + (5/7) * Q
Distribute: Q = (25/49)D + (25/49)Q + (5/7)Q
Combine like terms: Q - (25/49)Q - (5/7)Q = (25/49)D
Simplify: (49/49)Q - (25/49)Q - (35/49)Q = (25/49)D
Combine like terms: (35/49)Q = (25/49)D
Divide both sides by (25/49): (35/49)Q / (25/49) = (25/49)D / (25/49)
Simplify: Q = (5/7)D
6. Plug the ratio of D and Q back into equation 1 or equation 2 to find their values.
Using equation 1, D = (5/7) * (D + Q)
Substitute Q from the previous step into the equation:
D = (5/7) * (D + (5/7)D)
Simplify: D = (5/7) * (1 + 5/7)D
Distribute: D = (5/7) * (12/7)D
Simplify the right side: D = (60/49)D
7. Solve for D:
Divide both sides by D: D / D = (60/49)D / D
Simplify: 1 = 60 / 49
Multiply both sides by 49: 49 = 60
This equation is not true, so there is no unique solution.