Question

Question #55dec

Answer 1

The numbers are `14 and 18`

Explanation:

You can choose whether to use one or two variables.

I will use one variable and write the second number in terms of the first.

Let the smaller number be `x`
The larger number is `x+4` (They differ by `4`)

The sum is 32. Write an equation:

`x+x+4 =32`

`2x = 28`

`x=14`

The numbers are `14 and 18`

`18-14=4 and 14+18 = 32`

---

However, a question like this can be done by logic as well.

You know what the sum of the numbers is, and that one number is `4` more than the other.

Subtract the difference between them from `32` first.
`32-4 = 28`

This now has to be the sum of two equal numbers:
`28 div 2=14`

The one number is `14` and the other is `4` more, ie `18`

If you look at the process in this thinking, you will see that is exactly what was done with the algebra.

Answer 2

`18` and `14`

Explanation:

There are 2 ways you could solve this. The first is the proper way, but if it's with simple numbers, I use the second way. I'll show you both.

1st Way:

Let `x` and `y` be the two numbers.

Difference of `4:" "x-y=4`
The Sum is `32:" "x+y=32`

If we add the two equations together, we get:
`2x=36`

We can simplify this to:
`x=18`

By substituting `x` into either of the initial equations, we get:
`18+y=32`
`y=14`.

2nd Way:
Since the numbers are pretty small, I would do it like this mentally:

We know we need two numbers that add up to 32. Let's divide 32 by 2:

`32/2 = 16`.

Now, the difference between those two numbers is `4`.
So if we `+-2` to each side, we would get a difference of `4`.

`16+2=18`
`16-2=14`

Don't you think this is faster?!

But you should always know how to solve it using the first method as that is pure algebra.

Answer 3

`a = 18`
`b = 14`

Explanation:

Let `a` and `b` represent the two numbers.

Because you have two numbers, you will need two equations to find them.

Given in the problem are the following two equations:

1) The sum of `a` and `b` is `32`
`a + b = 32`

2) The difference between `a` and `b` is `4`
`a - b = 4`

Add the equations to let the `b` term drop out to zero

. .`a + b = 32`
+ `a - b =   4`
....................................
.`2a . . . . = 36`

`a = 18` `larr` answer for `a`

If `a = 18,` then `b = 14` `larr` answer for `b`

Answer:
`a = 18`
`b = 14`
~ ~ ~ ~ ~ ~ ~ ~

Check
. `a +   b = 32`
`18 + 14 = 32`  ✓

. `a -  b  = 4`
`18 - 14 = 4`  ✓