Question

Explain answer, will mark brainliest
Susie buys 2 pieces of salmon, each weighing x pounds, and 1 piece of trout, weighing y pounds, where x and y are integers. The salmon cost $3.50 per pound and the trout cost $5 per pound. If the total cost of the fish was $77, what is the value of y?

Answer 1

Answer:

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

Step-by-step explanation:

Answer 2

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.

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