Given expression for all coins is 0.05n + 0.10d +0.25q .
Total value of all coins = $3.25.
Therefore,
0.05n + 0.10d +0.25q = 3.25 ------------------(1)
Total number of coins = 31.
We can setup second equation as
n+d+q = 31. -----------------------(2).
Jessie has four more dimes than she does quarters.
Number of quarters = q.
Number of dimes is four more than number of quarter.
Therefore,
d = q + 4. ------------------------(3)
Substituting d=q+4 in first and second equation we get
0.05n + 0.10(q+4) +0.25q = 3.25 => 0.05n +0.10q + 0.40 +0.25q = 3.25
0.05n +0.35q = 3.25 - 0.40
0.05n +0.35q = 2.85. ------------------------(4)
n+d+q = 31 => n+ q+4 +q = 31.
n+2q =31 -4
n+2q = 27. ------------------------(5
Solving equation (5) for n
n = 27-2q.
Substituting n = 27-2q in (4) equation, we get
0.05(27-2q) +0.35q = 2.85
1.35 - 0.10q +0.35q = 2.85
1.35 +0.25q = 2.85
0.25q = 2.85 - 1.35
0.25q = 1.5.
Dividing both sides by 0.25, we get
q = 6.
Plugging q=6 in n = 27-2q, we get
n = 27 -2(6) = 27-12 = 15.
Plugging n=15 and q=6 in second equation n+d+q = 31.
15+d+6 = 31.
21 +d = 31.
Subtracting 21 from both sides, we get
21 +d -21= 31-21
d = 10.
