Pavel has $ 15.40 in dimes and quarters. He knows that he has three times as many dimes as quarters. He wants to create a system of equations to determine exactly how many dimes and how many quarters he has.
If d represents the number of dimes and q represents the number of quarters that Pavel has, which of the following systems of linear equations can be used to solve the given problem?
Let x represent the number of quarters that Pavel has.
Since Pavel has three times as many dimes as quarters, then he has 3x dimes.
Since a quarter is $0.25, then the value of the quarters is 0.25x dollars.
Since a dime is $0.10, then the value of the dimes is 0.10(3x) = 0.30x dollars.
Since Pavel has $15.40 in dimes and quarters, then we have the equation:
0.25x + 0.30x = 15.40
0.55x = 15.40
x = 15.40/0.55
x = <<28=28>>28
Therefore, Pavel has 28 quarters.
Since Pavel has three times as many dimes as quarters, then he has 3(28) = 84 dimes.
Therefore, Pavel has 84 dimes. Answer: \boxed{d = 84,\ q = 28}.