Jean has a total of 24 coins consisting of just quarters and nickels. The coins total $3.40. How many of them are quarters?
if there are x quarters, the rest (24-x) are nickels. Adding up their values, we get
25x + 5(24-x) = 340
x = 11
To find the number of quarters Jean has, we can set up a system of equations based on the given information.
Let's represent the number of quarters as "q" and the number of nickels as "n".
We know the total number of coins is 24, so we can write the equation:
q + n = 24 (Equation 1)
We also know that the total value of the coins is $3.40. Quarters have a value of 25 cents (or $0.25) each, and nickels have a value of 5 cents (or $0.05) each. So we can write another equation for the total value:
0.25q + 0.05n = 3.40 (Equation 2)
Now we have a system of two equations that we can solve to find the values of q and n.
First, let's solve Equation 1 for one variable in terms of the other. We can solve for q by subtracting n from both sides:
q = 24 - n
Substitute this value of q in Equation 2:
0.25(24 - n) + 0.05n = 3.40
Now, we can simplify and solve for n:
6 - 0.25n + 0.05n = 3.40
-0.20n = 3.40 - 6
-0.20n = -2.60
n = -2.60 / -0.20
n = 13
We have found that Jean has 13 nickels.
Now substitute this value of n back into Equation 1 to find q:
q + 13 = 24
q = 24 - 13
q = 11
Therefore, Jean has 11 quarters.