Answer:
Total value of nickels = $1.30
Step-by-step explanation:
let the number of nickels ($0.05) be "n" and the number of dimes ($0.10) be "d"
given that the total number of coins is 44, we can write :
number of nickels + number of dimes = 44 coins, or
n + d = 44 (rearranging this)
d = 44 - n --------> (eq 1)
we are also given that the total value of coins she has is $3.10.
Hence we can also write:
total value of nickels + total value of dimes = $3.10 ---------> (eq 2)
we know that the total value of nickels is the value of each nickel x number of nickels = $0.05n
Similarly, the total value of dimes is the value of each dime x number of dimes = $0.10d
if we substitute these values into eq 2, we get
0.05n + 0.10d = 3.10 --------> (eq 3)
we can now solve eq 1 and eq 3 by substitution.
substituting eq 1 into eq 3,
0.05n + 0.10d = 3.10
0.05n + 0.10(44-n) = 3.10
0.05n + 4.4 - 0.10n = 3.10
-0.05n + 4.4 = 3.10 (subtract 4.4 from both sides)
-0.05n = 3.10 - 4.4
-0.05n = -1.3 (divide both sides by -0.05)
n = -1.3 / -0.05
n = 26 (i.e she had 25 nickels)
Hence the value of nickels she has (using formula above)
= $0.05n
= $0.05 x 26
= $1.30
