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
To solve this problem, let's use variables to represent the number of nickels, dimes, and quarters in the jar.
Let's say:
n = number of nickels
d = number of dimes
q = number of quarters
We are given the following information:
1) There are twice as many nickels as there are quarters: n = 2q.
2) The value of dimes is $15.30: 0.10d = 15.30.
To find the number of quarters, we can set up an equation based on the total value of all the coins:
0.05n + 0.10d + 0.25q = 74.80.
Now, let's substitute the value of n from the first given information into this equation:
0.05(2q) + 0.10d + 0.25q = 74.80.
Simplifying this equation:
0.10q + 0.10d + 0.25q = 74.80,
0.35q + 0.10d = 74.80.
Next, let's substitute the value of d from the second given information into this equation:
0.35q + 0.10(153) = 74.80.
Simplifying further:
0.35q + 15.30 = 74.80,
0.35q = 74.80 - 15.30,
0.35q = 59.50.
Now, divide both sides of the equation by 0.35 to solve for q:
q = 59.50 / 0.35,
q = 170.
Therefore, there are 170 quarters in the jar.
n=2q
N*.05+15.30+.25q=74.80
2q(.05) +15.30+.25q=74.80
solve for number of qurters, q.