The sum of two numbers is 36. If the second number is four more than three times the first, find the numbers

Question

The sum of two numbers is 36. If the second number is four more than three times

the first, find the numbers

Answer 1

N + M = 36 (say M ≥ N)

M = 4+3N <<< from "... the second number is four more than three times the first..."

By substitution:

N + (4+3N) = 36

4N = 32

N = 8 ---> M = 28

Answer 2

Hello Ritumua!

I hope I can help you today.

So the problem states that the sum of two numbers is 36, and the second number is four more than three times the first, and asks us what the two numbers are.

The first thing we need to do is figure out what this all means algebraically.

In other words, we need to translate the English into algebra.

Let's do this one step at a time.

First we have two numbers. Let's give them names.

The first one we will call "n", the second we will call "m".

Now let's start translating the English into algebra.

The sum of the two numbers is 36.

This means when you add them together you get 36.

Since we gave them each a name (assigned them each to a variable), we can actually write this equation now.

n + m = 36

The first number "n" plus the second "m" is 36.

Now let's look at the next sentence.

If the second number is four more than three times the first, find the numbers.

Okay.

So the second number is four more than three times the first.

What does this mean? Well, if I have four more apples than you, then you add 4 to the number of apples you have to get the number I have.

So "four more than", refers to addition. (specifically to adding 4 to something)

The thing we are adding four to comes next:

"three times the first"

So we have two numbers, we called them n and m, and we said originally that n is the first number, and m the second.

Times means multiplication, and the first refers to n, so we have:

3×n.

So we have four more than three times the first => "add four to three times n"

=> 4 + 3×n

But we were told that "the second number equals four more than three times the first"

The second number is m.

So the expression 4 + 3n equals m.

m = 4 + 3n

Now we have two equations!

1.) n + m = 36

and

2.) m = 4 + 3n

We have two equations and two unknowns, so we can get rid of one of the unknowns and solve for the other.

There are several techniques we can use to accomplish this, but the easiest one (in this case) is substitution.

We could solve equation 1 if it was in terms of n only. In other words, if we could get rid of the m in the equation.

Luckily, equation 2 gives us m in terms of n. (it gives us something we can replace m with)

So we have:

n + m = 36

Replacing m with m = 4 + 3n

n + (4 + 3n) = 36

n + 4 + 3n = 36

Combining like terms

4n + 4 = 36

Subtracting by 4:

4n = 32

Dividing by 4

n = 8.

Yes! Now we have the first number. But how do we find the second number?

Well, we have two options.

We have 2 equations relating n and m, so we could plug in n = 8 into either of those and solve for m.

I'll illustrate both just for clarity:

Using equation 1:

n + m = 36

Replacing n with 8:

(8) + m = 36

Subtracting 8:

m = 28.

Using equation 2:

m = 4 + 3n

Replacing n with 8:

m = 4 + 3(8)

m = 4 + 24

m = 28

As you can see, either equation will work when solving for the second unknown.

So the first number is 8, and the second number is 28.

The trick to doing these problems is to assign the unknown numbers variables (like n and m) so we can translate the problem into algebra, translate the English into algebra, and then eliminate one of the variables so we can solve for the other one.

Then back-substitute (i.e. plug-in the value you found like we did with n = 8 in this problem) to find the value of the other unknown.

I hope this helps! Please let me know if you have any questions, or if anything was confusing or unclear.

I hope you have a great day!