SOLUTION: Maria needs $2.35 to buy a magazine. The only money she has is a jar of nickels and dimes. Write an equation in standard form for the different amounts of nickels x and dimes y s

0.05x + 0.10y = 2.35

Multiply through by 100

   5x + 10y = 235

Divide through by 5

     x + 2y = 47

You can have from 0 up to 23 dimes and the rest nickels.
So there are 24 possible solutions.


Solutions:

      y dimes and  x nickels. 
-----------------------------
 1.   0 dimes and 47 nickels.
 2.   1 dime  and 45 nickels.
 3.   2 dimes and 43 nickels.
 4.   3 dimes and 41 nickels.
 5.   4 dimes and 39 nickels.
 6.   5 dimes and 37 nickels.
 7.   6 dimes and 35 nickels.
 8.   7 dimes and 33 nickels.
 9.   8 dimes and 31 nickels.
10.   9 dimes and 29 nickels.
11.  10 dimes and 27 nickels.
12.  11 dimes and 25 nickels.
13.  12 dimes and 23 nickels.
14.  13 dimes and 21 nickels.
15.  14 dimes and 19 nickels.
16.  15 dimes and 17 nickels.
17.  16 dimes and 15 nickels.
18.  17 dimes and 13 nickels.
19.  18 dimes and 11 nickels.
20.  19 dimes and  9 nickels.
21.  20 dimes and  7 nickels.
22.  21 dimes and  5 nickels.
23.  22 dimes and  3 nickels.
24.  23 dimes and  1 nickel.

Edwin