Question

jessie has some nickels, dimes, and quarters in her bank. The number of coins is 31. The expression 0.05n + 0.10d +0.24q represents the value of the coins, which is $3.25. Jessie has four more dimes than she does quarters. How many of each coin does Jessie have?

Answer 1

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.

Therefore, number of dimes = 10, number of quarters = 6 and number of nickels = 15.