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If each term in the sum a1+a2+a3+...+an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?A. 38B. 39C. 40D. 41E. 42

User Jan Swart
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1 Answer

1 vote

Answer:

C. 40

Explanation:

Let us say there are x 7's and y 77's.

We have been given that each term in the sum a1+a2+a3+...+an is either 7 or 77 and the sum equals 350. We are asked to find the value of n.

Since the sum of all numbers is 350, so we can represent this information in an equation as:


7x+77y=350

The only integer solutions for the equation
7x+77y=350 are 10, 20, 30, 40, 50 .

So, there can be these many terms: 10 or 20 or 30 or 40 or 50 .

The given option only contains 40, so 40 would be the answer. For 40 terms to be there, there has to be 39 sevens and 1 seventy-seven.

Let us verify our answer.


7x+77y=350


7(39)+77(1)=350


273+77=350


350=350

Therefore, the total terms (n) could be equal to 40 and option C is the correct choice.

User Mosquito Mike
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