Question

Jake had a piggy bank dipped with nickels quarters and dimes. He noted that he had three times as many dimes as quarters and four less than twice the number of dimes in nickels. Jake knee the total in the piggy bank was $20.20 what was his value in dimes ?

Answer 1

Answer:

There are 72 dimes having a total value of $7.2.

Step-by-step explanation:

Let the number of dimes be 'd', nickels be 'n' and quarters be 'q'.

Given:

Number of dimes is three times quarters

Number of nickels is four less than twice the number of dimes.

Total amount in the piggy bank is $20.20

Now, as per question:

Number of dimes is three times quarters

Framing in equation form, we get:

$d=3\times q\\d=3q\\q=\frac{d}{3}---1$

Number of nickels is four less than twice the number of dimes.

Framing in equation form, we get:

$n=2d-4----2$

Now, value of 1 dime in dollars is 0.1.

Value 'd' dimes = $0.1d ----------(A)

Value of 1 quarter = $0.25

Value of 'q' quarters = $0.25q ----------(B)

Value of 1 nickel = $0.05

Value of 'n' nickels = $0.05n ----------(C)

Now, total amount is equal to the sum of all the amounts of each type of coin.

So, adding equations (A), (B) and (C) and equating to 20.20, we get:

$0.1d+0.25q+0.05n=20.20$

Now, using equations (1) and (2), the above equation can be rewritten as:

$0.1d+0.25(\frac{d}{3})+0.05(2d-4)=20.20\\\\0.1d+\frac{d}{12}+0.1d-0.2=20.20\\\\d(0.1+0.1+\frac{1}{12})=20.20+0.2\\\\0.2833d=20.40\\\\d=\frac{20.40}{0.2833}=72$

So, there are 72 dimes in the piggy bank.

Total value of 72 dimes = 72(0.1) = $7.2