The Jaspers collect nickels, dimes, and quarters in a jar. When they count the change in the jar, there are twice as many nickels as there are quarters. If there is $15.30 in dimes and $74.80 in all, how many quarters are there. Please include an equation and steps.
Let's assume the number of quarters in the jar is "Q".
We are given that there are twice as many nickels as there are quarters. So, the number of nickels would be 2Q.
Now, let's calculate the total value of the dimes. We are given that there is $15.30 in dimes. We know that each dime is worth $0.10, so we can divide the total value by the value of each dime: $15.30 / $0.10 = 153 dimes.
Similarly, we know that each nickel is worth $0.05. So, the value of all nickels would be 2Q * $0.05 = $0.10Q.
The value of all quarters would be Q * $0.25.
Finally, we know that the total value of all coins is $74.80. So, putting it all together, we can create an equation:
Value of dimes + Value of nickels + Value of quarters = $74.80
$15.30 + $0.10Q + $0.25Q = $74.80
Simplifying the equation, we get:
$15.30 + $0.35Q = $74.80
To solve for Q, we need to isolate it on one side of the equation. Subtracting $15.30 from both sides gives:
$0.35Q = $74.80 - $15.30
$0.35Q = $59.50
Dividing both sides by $0.35, we get:
Q = $59.50 / $0.35
Q ≈ 170
Therefore, there are approximately 170 quarters in the jar.