Question

The sum of 3 integers is 44. The sum of the first and second integers exceeds by the third by 98. The third integer is 92 less than the first. Find the 3 integers.

Answer 1

Let's simplify the word problem into numbers:\[a+b+c = 44\]\[a + b =c + 98\]\[c = a-92\]Does that make sense so far?

Answer 2

yes

Answer 3

So which way would you like to solve this problem? You can do so through substitution (easiest), system of linear equations, or Gaussian elimination.

Answer 4

yes, substitution please

Answer 5

Substituting the 3rd equation, c = a - 92, into the first two equations, you find:\[a + b + (a - 92) = 44\] and \[a + b = (a-92) + 98\]

You can easily solve the second equation, and then afterwards, you can solve the first.

Answer 6

could you please show how to solve the second equation?

Answer 7

Sure, the second equation is:\[a + b = a - 92 + 98\]Since -92 + 98 = 98 - 92 = 6, we see:\[a + b = a + 6\]Simply subtract a from both sides:\[b = 6\]

Answer 8

I got it thank youu!! :)