Destiny has 5 times as many quarters as dimes. If the total of the coin was $16.20 how many of each coin does she have

Question

Destiny has 5 times as many quarters as dimes. If the total of the coin was $16.20 how many of each coin does she have

 

Answer 1

this is a system of equations question! Imagine the problem as two smaller problems

how many quarters to dimes she has q/5 (she needs 5 quarters to make 1 dime) = d or q = 5d

and the sum of both numbers in terms of their value .25q+.10d = 16.20

to solve this question we can use substitution replacing q in the second equation with 5d

.25*5d + .10*d = 16.20

this makes 1.25d+.1d or 1.35d = 16.20

solving by dividing by 1.35 gives us d = 12

so she has 12 dimes and thus 5*12 = 60 quarters

 

Answer 2

  Let d = number of dimes

5d = number of quarters

The equation will deal with the value of the coins, not just the number. Each dime is worth .10, each quarter is worth .25

.10d + .25(5d) = 16.20 Multiply each side by 100

10d + 25(5d) =1620

10 d + 125 d = 1620

135d = 1620

d = 12 dimes

5(12) = 60 quarters 

 

Check by plugging values into equation.