What is the Sum of Positive Integers a, b, and c Given a Specific Equation?

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In summary, the sum of a, b and c is the total of all three numbers added together. Finding the sum of a, b and c is important in determining the total quantity or value of multiple numbers. To find the sum of a, b and c, simply add all three numbers together, regardless of the order. Even if one or more numbers is negative, the sum will still be calculated in the same way. The sum of a, b and c can also be a decimal or fraction if one or more numbers is a decimal or fraction, in which case appropriate rules must be followed for adding them.
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If $a,\,b$ and $c$ are positive integers such that $16a b c+4a b+4a c+4b c+ a+b+c =4561$, find the sum of $a+b+c$.
 
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anemone said:
If $a,\,b$ and $c$ are positive integers such that $16a b c+4a b+4a c+4b c+ a+b+c =4561$, find the sum of $a+b+c$.

multiply by 4 and add 1 to get
$(4a+1)(4b+1)(4c+1) = 4 * 4561+1 = 5 * 41 * 89$
giving
$a=1;b=10;c=22$ or any permutation or $a+b+c= 33$
 
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Thanks, kaliprasad for your participation and the correct solution! Very well done!:)
 

FAQ: What is the Sum of Positive Integers a, b, and c Given a Specific Equation?

What is the sum of a, b and c?

The sum of a, b and c is the total of all three numbers added together. It is calculated by adding a to b, and then adding the result to c.

Why is finding the sum of a, b and c important?

Finding the sum of a, b and c is important because it helps us determine the total quantity or value of multiple numbers. This can be useful in various fields such as mathematics, physics, and economics.

How do I find the sum of a, b and c?

To find the sum of a, b and c, simply add all three numbers together. You can use a calculator or manually add the numbers. The order in which you add the numbers does not matter, as the sum will be the same.

What if a, b or c is a negative number?

The sum of a, b and c will still be calculated in the same way, regardless of whether one or more numbers is negative. However, the result may also be negative, depending on the numbers and their values. For example, -2 + 5 + 3 would result in a sum of 6.

Can the sum of a, b and c be a decimal or fraction?

Yes, the sum of a, b and c can be a decimal or fraction if one or more of the numbers is a decimal or fraction. When adding decimals or fractions, it is important to follow the appropriate rules for adding them, such as finding a common denominator. The result may also need to be rounded to a certain number of decimal places or simplified as a fraction.

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