he has $3.45 in changeHe has fourfour more quarters than dimes but fourfour times as many nickels as quarters. How many coins of each type does he​ have?

Question

How many dimes and how many quarters does he have

Answer 1

25Q + 10D + 5N = 345 <--- amounts are in pennies

 

Q  = D+4 <--- 4 more quarters than dimes

 

N = 4Q = 4(D+4) = 4D + 16 <---   4 times as many nickles as quarters; substitutes Q=D+4

                                                     so as to get nickles in terms of dimes

 

Substitutes the 2nd and 3rd equation into the 1st equation

25(D+4) + 10D + 5(4d+16) = 345

 

25D + 100 + 10D + 20d + 80 = 345

 

55d + 180 = 345

 

55d = 165

 

d = 3

 

3 dimes

7 quarters

28 nickels

 

3 x 10 + 7 x 25 + 5 x 28 = 345; yes it checks