SOLUTION: Susie buys 2 pieces of salmon, each weighing x pounds, and 1 piece of trout,y pounds, where x and y are integers. The salmon costs $3.50 per pound and the trout costs $5 per pound.

Question 1121103: Susie buys 2 pieces of salmon, each weighing x pounds, and 1 piece of trout,y pounds, where x and y are integers. The salmon costs $3.50 per pound and the trout costs $5 per pound. If the total cost of the fish was $77, what could be the value of y?
Found 2 solutions by solver91311, greenestamps:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

2 times 3.50 times is the amount spent on salmon. 5 times is the amount spent on trout and the total amount spent is 77.

Which will be more convenient to represent as:

Since the weights in this problem must be positive integers, the smallest possible value for either or would be 1.

Clearly, if , then , and we have one possible answer.

We know that because is not evenly divisible by 5.

Note that for to have an integer solution, where . But our previous work bounds the possible values for between 1 and 14, so the only two possible values are 7 and 14.

Hence, 12 lbs salmon and 7 lbs trout, or 2 lbs salmon and 14 lbs trout.

John

My calculator said it, I believe it, that settles it

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The amount spent on salmon is 7x; the amount spent on trout is 5y. The total amount spent is 77:

Very informally....

Since x and y are positive integers, 7x is a multiple of 7. Then, since 77 is a multiple of 7, 5y must also be a multiple of 7.

Since 5 is not a multiple of 7, y must be. So the possible values of y are 7, 14, 21, ....

But y has to be less than 77/5 = 15.4; so the only two possible values for y are 7 and 14.

Answer: The two possible values for y are 7 and 14.

The same solution, using formal mathematics....

Since 5 is not a multiple of 7, y must be.

Then, as above, the constraints on the value of y lead to exactly two possible values of y -- 7 and 14.

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