Question

Priam has dimes and pennies in a cup holder in his car. The total value of the coins is $4.21. The number of dimes is three less than four times the number of pennies. How many dimes and how many pennies are in the cup?

Answer 1

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 :_

$d=4p-3..................(1)\\\\0.1d+0.01p=4.21...........(2)$

Substitute the value of d from (1) in equation (2), we get

$0.1(4p-3)+0.01p=4.21\\\\\Rightarrow\ 0.4p-0.3+0.01p=4.21\\\\\Rightarrow\ 0.41p=4.21+0.3\\\\\Rightarrow\ 0.41p=4.51\\\\\Rightarrow\ p=\dfrac{4.51}{0.41}=11$

Then , Put value of p in (1), we get

$d=4(11)-3=44-3=41$

Hence, there are 41 dimes and 11 pennies in the cup.