Respuesta :
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:
[tex]d=3\times q\\d=3q\\q=\frac{d}{3}---1[/tex]
Number of nickels is four less than twice the number of dimes.
Framing in equation form, we get:
[tex]n=2d-4----2[/tex]
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:
[tex]0.1d+0.25q+0.05n=20.20[/tex]
Now, using equations (1) and (2), the above equation can be rewritten as:
[tex]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[/tex]
So, there are 72 dimes in the piggy bank.
Total value of 72 dimes = 72(0.1) = $7.2
