Question 1099636
d = no. dime; q = no. of quarters; h = no. of half dollars
:
Write an equation for each statement
:
Alice has saved 5.00 in dimes, quarters, and half dollars.
.10d + .25q + .50h = 5.00
:
 She finds that she has 30 coins altogether
d + q + h = 30
:
 there are four times as many quarters as there are half dollars.
q = 4h
 In the 2nd equation, replace q with 4h
d + 4h + h = 30
d + 5h = 30
d = (30-5h)
In the 1st equation replace d with (30-5h)
.10(30-5h) + .25q + .50h = 5.00
3 - .5h + .25q + .50h = 5.00
.50h - .50h + .25h = 5 - 3
.25q = 2
q = 2/.25
q = 8 quarters
:
In the equation d + q + q = 30, replace q with 8
d + 8 + h = 30
d + h = 30 - 8
d + h = 22
Replace d = (30-5h)
30 - 5h + h = 22
-5h + h = 22 - 30
-4h = -8
h = -8/-4
h = 2 half dollars
Find d
d + 2 = 22
d = 22 - 2
d = 20 dimes



 How many dimes does Alice have ?