Uncle Hank has another riddle for his nephew's. He tells them, "I have the sms number of nickels and pennies. I have 4 times as many quarters as nickels. I have 3 more dimes than quarters. I have a total of $6.14." Ben has started the equation for slicing the riddle which is "0.01p+" finish writing the equation that represents the riddle. How many of each type of coin does Uncle Hank have?

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chitalopez2006 chitalopez2006

31-01-2020
Mathematics

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Uncle Hank has another riddle for his nephew's. He tells them, "I have the sms number of nickels and pennies. I have 4 times as many quarters as nickels. I have 3 more dimes than quarters. I have a total of $6.14." Ben has started the equation for slicing the riddle which is "0.01p+" finish writing the equation that represents the riddle. How many of each type of coin does Uncle Hank have?

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iwillanswer iwillanswer · Answer 1 · 2020-02-07T09:48:57+01:00

Uncle Hank has 4 pennies, 4 nickels, 16 quarters and 19 dimes

Solution:

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

I have the same number of nickels and pennies

n = p ------- eqn 1

I have 4 times as many quarters as nickels

Number of quarters = 4 times the number of nickels

q = 4n -------- eqn 2

I have 3 more dimes than quarters

d = 3 + q

Substitute eqn 2 in above

d = 3 + 4n ------- eqn 3

I have a total of $6.14

$ 6.14 is equal to 614 cents

Thus, we frame a equation as,

[tex]1 \times p + 5 \times n + 25 \times q + 10 \times d = 614[/tex]

p + 5n + 25q + 10d = 614 ------ eqn 4

Substitute eqn 1 in above

n + 5n + 25q + 10d = 614

Substitute eqn 2 in above

n + 5n + 25(4n) + 10d = 614

n + 5n + 100n + 10d = 614

Substitute eqn 3 in above

n + 5n + 100n + 10(3 + 4n) = 614

Simplify the above expression

106n + 30 + 40n = 614

146n = 584

Divide both sides by 146

n = 4

From eqn 1,

n = p

p = 4

Substitute n = 4 in eqn 2

q = 4n = 4(4)

q = 16

Substitute n = 4 in eqn 3

d = 3 + 4n

d = 3 + 4(4)

d = 19

Thus Uncle Hank has 4 pennies, 4 nickels, 16 quarters and 19 dimes