SOLUTION: Betty has $20 in dimes, quarters, and half dollars. She has 110 coins in all. There are 2 less dimes than six times the number of half dollars. How many of each coin does she hav
Algebra ->
Customizable Word Problem Solvers
-> Coins
-> SOLUTION: Betty has $20 in dimes, quarters, and half dollars. She has 110 coins in all. There are 2 less dimes than six times the number of half dollars. How many of each coin does she hav
Log On
Question 549337: Betty has $20 in dimes, quarters, and half dollars. She has 110 coins in all. There are 2 less dimes than six times the number of half dollars. How many of each coin does she have? Found 2 solutions by TutorDelphia, Edwin McCravy:Answer by TutorDelphia(193) (Show Source):
You can put this solution on YOUR website! There's lots of info here, lets break it down into some different equations
Lets have
d=dimes
q=quarters
h=half dollars
We also know
d+q+h=110
And we have that 6*h-2=d
so
d=6*h-2
and
6*h-2+q+h=110
7h+q=112
So now we have two equations with two variables
20.2=1.1h+.25q
7h+q=112
Lets use substitution to solve
q=112-7h
20.2=1.1h+.25*(112-7h)
20.2=1.1h+28-1.75h
-7.80=-.65h
h=12
q=112-7h
q=112-7*12
q=28
d+q+h=110
d+28+12=110
d=70
There are 2 less dimes than six times them number of half dollars.
d = 6h - 2
So we have this system of equations:
10d + 25q + 50h = 2000
d + q + h = 110
d = 6h - 2
Arrange them like this:
10d + 25q + 50h = 2000
d + q + h = 110
d - 6h = -2
Can you solve that system? If not post again asking how.
Solution:
d = 70, q = 28 and h = 12
So there are 70 dimes, 28 quarters and 12 half dollars.
Checking:
70 dimes makes $7
28 quarters makes $7
12 half dollars makes $6
--------------------------
110 coins makes $20
Six times the number of half dollars = 6×12 = 72
2 less than 72 is 70 and that is the number of dimes.
Edwin
