SOLUTION: If someone could please help me with this question: Joe has three times as many dimes as Dave. Dave has six more quarters than Joe. Joe has as many quarters as Dave does dimes. If

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Question 940200: If someone could please help me with this question: Joe has three times as many dimes as Dave. Dave has six more quarters than Joe. Joe has as many quarters as Dave does dimes. If the value of Joe's dimes is the same as Dave's quarters, how many dimes does Dave have?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Joe has three times as many dimes as Dave. Dave has six more quarters than Joe. Joe has as many quarters as Dave does dimes. If the value of Joe's dimes is the same as Dave's quarters, how many dimes does Dave have?
Suppose Joe has x quarters
Suppose Joe has y dimes worth 10y cents
Suppose Dave has z quarters worth 25z cents
Suppose Dave has w dimes

Joe has three times as many dimes as Dave. 
y = 3w

Dave has six more quarters than Joe. 
z = x+6

Joe has as many quarters as Dave does dimes. 
x = w

the value of Joe's dimes is the same as Dave's quarters, 
10y = 25z

We have this system:

system%28y+=+3w%2Cz+=+x%2B6%2Cx+=+w%2C10y+=+25z%29

Substitute x for w

system%28y+=+3x%2Cz+=+x%2B6%2C10y+=+25z%29

Substitute x+6 for z

system%28y+=+3x%2C10y+=+25%28x%2B6%29%29

Substitute 3x for y

10%283x%29=25%28x%2B6%29

30x=25x%2B150

5x=150

x=30

Substitute in y = 3x

y=3%2830%29
y=90

Substitute in z = x+6

z+=+30%2B6
z=36

and since x = w,

w=30

Joe has 30 quarters
Joe has 90 dimes worth 10(90) or 900 cents, or $9
Dave has 36 quarters worth 25(36) or 900 cents, or $9
Dave has 30 dimes

how many dimes does Dave have?
Dave has 90 dimes.

Edwin