SOLUTION: Sanjay has as many nickels as Doug has dimes; Doug has twice as many nickels as Sanjay has dimes. If together they have $2.50 in nickels and dimes, how many nickels does Sanjay hav

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Question 1117403: Sanjay has as many nickels as Doug has dimes; Doug has twice as many nickels as Sanjay has dimes. If together they have $2.50 in nickels and dimes, how many nickels does Sanjay have?
A) 1 nickel
B) 4 nickels
C) 7 nickels
D) 10 nickels
E) The answer cannot be determined from the given information.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630) About Me  (Show Source):
Answer by ikleyn(52914) About Me  (Show Source):
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.
Let x = #of Doug's    dimes,   and

    y = #of Sanjay's  dimes.


Then, according to the condition,  

   x = #of Sanjay's nickels and  2y = #of Doug's nickels


From there, you have this equation for the total in cents

   10x + 5x + 10y + 5*(2y) = 250   cents,   or

   15x + 20y = 250.


It is a Diophantine equation (the solutions must be positive integers).

And there are no any other conditions/equations.


All possible solutions to eq(1) are in this Table


    x     y
-------------

   14     2
  
   10     5

    6     8

    2     11


Of all possible given options only option  D) 10 nickels of Sanjay  works.


Other offered options  A), B), and C)  do not work.

Answer.   Of the four offered/asked options only option  D)  works. 

Notice.   Other solutions are possible, listed in the Table.

          But since they do not match to offered options, I do not consider them as the answers to the problem's question.