Uncle Hank has 4 pennies, 4 nickels, 16 quarters and 19 dimes
<em><u>Solution:</u></em>
Let "n" be the number of nickels
Let "q" be the number of quarters
Let "p" be the number of pennies
Let "d" be the number of dimes
We know that,
a penny = 1 cent
a nickel = 5 cent
a Quarter = 25 cent
a Dime = 10 cent
<em><u>I have the same number of nickels and pennies</u></em>
n = p ------- eqn 1
<em><u>I have 4 times as many quarters as nickels</u></em>
Number of quarters = 4 times the number of nickels
q = 4n -------- eqn 2
<em><u>I have 3 more dimes than quarters</u></em>
d = 3 + q
<em><u>Substitute eqn 2 in above</u></em>
d = 3 + 4n ------- eqn 3
<em><u>I have a total of $6.14</u></em>
$ 6.14 is equal to 614 cents
Thus, we frame a equation as,
p + 5n + 25q + 10d = 614 ------ eqn 4
<em><u>Substitute eqn 1 in above</u></em>
n + 5n + 25q + 10d = 614
<em><u>Substitute eqn 2 in above</u></em>
n + 5n + 25(4n) + 10d = 614
n + 5n + 100n + 10d = 614
<em><u>Substitute eqn 3 in above</u></em>
n + 5n + 100n + 10(3 + 4n) = 614
<em><u>Simplify the above expression</u></em>
106n + 30 + 40n = 614
146n = 584
Divide both sides by 146
<h3>n = 4</h3>
From eqn 1,
n = p
<h3>p = 4</h3>
Substitute n = 4 in eqn 2
q = 4n = 4(4)
<h3>q = 16</h3>
Substitute n = 4 in eqn 3
d = 3 + 4n
d = 3 + 4(4)
<h3>d = 19</h3>
Thus Uncle Hank has 4 pennies, 4 nickels, 16 quarters and 19 dimes