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.
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To find the number of quarters, let's start by setting up equations based on the given information:
Let:
N = number of nickels
D = number of dimes
Q = number of quarters
We are given two pieces of information:
1. "When they count the change in the jar, there are twice as many nickels as there are quarters":
N = 2Q
2. "There is $15.30 in dimes and $74.80 in all":
0.05N + 0.10D + 0.25Q = 74.80 (equation for the total value of coins)
0.10D = 15.30 (equation for the value of dimes)
Now, let's solve the equations step by step:
1. Substitute the value of N from equation 1 into equation 2:
0.05(2Q) + 0.10D + 0.25Q = 74.80
2. Simplify the equation:
0.10Q + 0.10D + 0.25Q = 74.80
3. Combine like terms:
0.35Q + 0.10D = 74.80
4. Substitute the value of D from equation 2 into the simplified equation:
0.35Q + 0.10(15.30) = 74.80
5. Simplify the equation:
0.35Q + 1.53 = 74.80
6. Subtract 1.53 from both sides of the equation:
0.35Q = 73.27
7. Divide both sides of the equation by 0.35:
Q = 209
So, there are 209 quarters in the jar.