find two consecutive integers whose sum is 35

Question

im really bad at math and need help on my math homework

Answer 1

So let's break this down algebraically; in terms of variables.

We know that we have two integers (which just means whole numbers). Let's call them x and y.

We know that the sum of those two numbers is 35. So x + y = 35.

We also know that the two integers are consecutive, meaning one immediately follows the other. In any case, in order to get from one whole number to the next that follows, all we need to do is add 1. For example, the next consecutive whole number after 5 is 6. To get from 5 to 6, we just add 1: 5 + 1 = 6.

The key to solving this problem is generalizing that fact. Since the rule works for literally any two consecutive integers (25 + 1 = 26, 100 + 1 = 101), we can just say that x is our smaller integer and y is our larger, giving us x + 1 = y. If that sounds like madness to you, play with it for a second; punch in any whole number you can think of for x and confirm that y turns out to be the next consecutive integer!

This gives us a system of equations: multiple, different equations using the same variables:

x + y = 35

x + 1 = y

Since these are using the exact same variables, we're free to do substitution! And what's more, the bottom equation defines y in terms of x, meaning we can replace the y in the top equation with left side of the bottom:

x + y = 35

becomes

x + (x + 1) = 35

Now we can solve. Adding like terms:

2x + 1 = 35

-1 -1 isolate the variable by subtracting away the constant

-------------------

2x = 34

/2 /2 turn 2x into just x by dividing out the 2

-------------------

x = 17

With x in hand, we just go back to our other equation to find y:

x + 1 = y

becomes

17 + 1 = y

meaning

y = 18

Answer 2

Hey,

The answer would be 17 and 18. The simple way is to divide 35 by 2 i.e,

35/2 = 17.5 and take the preceding and succeeding whole numbers. In this case, 17 and 18.

Then get the sum! :)