how many denomination of each coins

Question

a man has a box of coins that he uses when playing poker with friends. The box currently contains 39 coins, consisting of pennies, dimes and quarters. The number of pennies is equal to the number of dimes and the total value is 2.73. How many of each denomination of coins does he have?

Answer 1

p + d + q = 39

p =d

.01p + .10d + .25q = 2.73

 

1) Plug in eq 2 into eq 1.

 

d + d + q = 39

2d + q = 39

q = 39 - 2d

 

2) Now we can solve for q in eq 3.

 

.01(d) + .10d + .25(39-2d) = 2.73

.01d + .1d + 9.75 - .5d = 2.73

-.39d = -7.02

d=18

 

3) Now use d to find q and p.

 

q = 39 - 2(18)

q = 3

 

p=d

p=18

 

4) Now plug them back into all 3 equations to check your work.

 

18 + 18 + 3 = 39

39 = 39

p =d

18=18

.01(18) + .10(18) + .25(3) = 2.73

.18 + 1.8 + .75 = 2.73

2.73 = 2.73