Answer: There are 41 dimes and 11 pennies in the cup.
Step-by-step explanation:
We know that 1 dime = 0.1 dollars
1 penny = 0.01 dollars
Let p be the number of pennies and d be the number of dimes.
Then we have the following equations :_
[tex]d=4p-3..................(1)\\\\0.1d+0.01p=4.21...........(2)[/tex]
Substitute the value of d from (1) in equation (2), we get
[tex]0.1(4p-3)+0.01p=4.21\\\\\Rightarrow\ 0.4p-0.3+0.01p=4.21\\\\\Rightarrow\ 0.41p=4.21+0.3\\\\\Rightarrow\ 0.41p=4.51\\\\\Rightarrow\ p=\dfrac{4.51}{0.41}=11[/tex]
Then , Put value of p in (1), we get
[tex]d=4(11)-3=44-3=41[/tex]
Hence, there are 41 dimes and 11 pennies in the cup.
