70 coins Some are quarters and rest are half dollars.

Question

70 Coins, Some are quarters, rest are half dollars if total value is $21.50, how many denominations does she have of quarters in piggy bank and half dollars in piggy bank?

Answer 1

Q = number of quarters

H = number of half-dollars

 

Set up a system of 2 linear equations in 2 unknowns Q and H:

 

Q + H = 70

(0.25)Q + (0.50)H = 21.5

 

You can solve by substitution.  From top equation get Q = 70 - H and plug into bottom equation.

 

(0.25)((70 - H) + (0.50)H = 21.50

17.5 - 0.25H + 0.50H = 21.50

0.25H = 4

H = 4/0.25 = 16

Q = 70 - H = 70 - 16 = 54

 

There are 54 quarters and 16 half-dollars.

 

Test the solution.