Question 1110652: Sally bought some white envelopes at $.02 per envelope and some blue envelopes at $.035 per envelope. Total cost was $240.50. How many of each envelope did she buy?
Most of these types of problems contain the total number of envelopes bought.
This one doesn't.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620)   (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
With only this information, you can't find a single solution. But you can find a finite set of solutions knowing that the numbers of white and blue envelopes must be whole numbers.
In this equation, 4w and 48100 are multiples of 4, so 7b must be a multiple of 4. Then, since 4 and 7 have no common factor, b must be a multiple of 4.
So b can be any multiple of 4 for which 7b is no more than 48100; and for each of those values of b the value of w is determined.
Note that each time you add 4 to the value of b, the value of w has to decrease by 7 for the sum of 4w and 7b to remain the same.
So to make a complete list of the solutions, you could start with b=0, which gives x=12025; then repeatedly increase b by 4 and decrease w by 7 until the value of w becomes negative.
(b,w) =
(0,12025)
(4,12018)
(8,12011)
(12,12004)
...
etc.
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