Question 231061
f = number of dollars
h = number of half dollars
q = number of quarters
d = number of dimes
n = number of nickels
p = number of pennies.


total money equals $10.00


f * 1 = amount of money in dollars
h * .5 = amount of money in half dollars
q * .25 = amount of money in quarters
d * .1 = amount of money in dimes
n * .05 = amount of money in nickels
p * .01 = amount of money in pennies


Total money collected equals $10.00


1*f + .5*h + .25*q + .10*d + .05*n + .01*p = 10


f and p are equal to 0, so this equation becomes:


1*0 + .5*h + .25*q + .10*d + .05*n + .01*0 = 10


Simplify this equation to get:


.5*h + .25*q + .10*d + .05*n = 10


Since:


q = 2*h (number of quarters equals 2 times the number of half dollars)
d = 2*q (number of dimes equals 2 times the number of quarters)
n = 3*d (number of nickels equals 3 times the number of dimes)


Replace n with 3*d to get:


.5*h + .25*q + .10*d + .05*3*d = 10


Replace d with 2*q to get:


.5*h + .25*q + .10*2*q + .05*3*2*q = 10


Replace q with 2*d to get:


.5*h + .25*2*h + .10*2*2*h + .05*3*2*2*h = 10


Simplify to get:


.5*h + .5*h + .4*h + .6*h = 10


Combine like terms to get:


2*h = 10


Divide both sides by 2 to get:


h = 5


Since q = 2*h, then q = 10
Since d = 2*q, then d = 20
Since n = 3*d, then n = 60


You have:


h = 5 * .5 = $2.50
q = 10 * .25 = $2.50
d = 20 * .1 = $1.00
n = 60 * .05 = $3.00

Total = $10.00 which is correct.


Cashier gets:


5 half dollars
10 quarters
20 dimes
60 nickels