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.
5 dimes and 7 quarters adds to 2.25
15.75/2.25 = 7
So, there are 7 times as many coins as that.
To find the total amount in quarters, we first need to determine the individual value of a dime and a quarter.
Let's assign a variable to the value of a dime. Let's say a dime is worth "x" dollars.
Therefore, a quarter will be worth "x" * 2.5 (since a quarter is 2.5 times more valuable than a dime).
Now, let's set up an equation to represent the total value in the piggy bank:
5x (the value of dimes) + 7(x * 2.5) (the value of quarters) = $15.75
Simplifying the equation, we get:
5x + 17.5x = 15.75
22.5x = 15.75
Solving for x:
x = 15.75 / 22.5
x = 0.7
So a dime is worth $0.70, and a quarter is worth $0.70 * 2.5 = $1.75.
To find the total amount in quarters, we multiply the value of a quarter ($1.75) by the number of quarters represented by the ratio of 7:
Total amount in quarters = 7 * $1.75 = $12.25
Therefore, the total amount in quarters is $12.25.