SOLUTION: If Juan has 4 more than twice the amount of nickels as sam and carlos has 2 less than 3 times the amount of nickels as sam and the total value of all 3 boys is 1.90, than how many

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Question 218682: If Juan has 4 more than twice the amount of nickels as sam and carlos has 2 less than 3 times the amount of nickels as sam and the total value of all 3 boys is 1.90, than how many nickels does sam have?
so far i am trying to set up the problem...
s=sam, c=carlos, j=juan
j=2(sam amount)+ 4
c=3(sam amount)-2
total= 1.90
there are 38 nickels...
please help..thanks
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let j = number of nickels Juan has
Let s = number of nickels Sam has
Let c = number of nickels Carlos has
given:
(1) j+=+2s+%2B+4
(2) c+=+3s+-+2
(3) j+%2B+s+%2B+c+=+190%2F5 (in nickels)
Substitute (1) and (2) in (3)
2s+%2B+4+%2B+s+%2B+3s+-+2+=+190%2F5
6s+%2B+2+=+190%2F5
6s+=+38+-+2
6s+=+36
s+=+6
Sam has 6 nickels
check answer:
and
j+=+2s+%2B+4
j+=+2%2A6+%2B+4
j+=+16
also
c+=+3s+-+2
c+=+3%2A6+-+2
c+=+16
and
j+%2B+s+%2B+c+=+190%2F5
16+%2B+6+%2B+16+=+190%2F5
38+=+38
OK

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
If Juan has 4 more than twice the amount of nickels as sam and carlos has 2 less than 3 times the amount of nickels as sam and the total value of all 3 boys is 1.90, than how many nickels does sam have?

Let amount of nickels that Sam has be S
Since Juan has 4 more than twice Sam's amount, then Juan has 2S + 4
Since Carlos has 2 less than 3 times Sam's amount, then Carlos has 3S - 2

Together, the 3 boys have: S + 2S + 4 + 3S - 2, or (6S + 2) nickels

Now, since the value of all their nickels is $1.90, then we have:

.05(6S + 2) = 1.9

.3S + .1 = 1.9

.3S = 1.8

Therefore, S+=+1.8%2F.3, which means that Sam has highlight_green%286%29 nickels.