If 4m + 6n = 10, what is 2m + 3n? Step by Step

Step by step

The question

Question: if 4m + 6n = 10, what is 2m + 3n?

4m + 6n = 10

We want 2m + 3n.

Let's look for it inside the equation.

2m + 3n = ?

1 Compare the two

Look at 4m + 6n and 2m + 3n.

We compare them part by part.

4 divided by 2 is 2.

So 4m is 2 times 2m.

4 ÷ 2 = 2, so 4m = 2 × 2m

6 divided by 3 is 2.

So 6n is 2 times 3n.

6 ÷ 3 = 2, so 6n = 2 × 3n

Every part of 4m + 6n is 2 times a part of 2m + 3n.

2 Take out the 2

So we can write each part as 2 times.

2 × 2m + 2 × 3n = 10

2 times each part is the same as 2 times the whole bracket: 2(2m + 3n).

Opening the bracket gives 4m + 6n back.

2(2m + 3n) = 10

3 Remove the 2

2(2m + 3n) means 2 times the bracket.

To remove times 2, we divide by 2.

We do it on both sides, so they stay equal.

2(2m + 3n)2 = 102

2 divided by 2 is 1.

So just the bracket is left.

10 divided by 2 is 5.

102 = 5

So 2m + 3n = 5!

2m + 3n = 5

Careful!

Both sides are divided by 2.

10 becomes 5.

Careful: not 2m + 3n = 10 ✗

4 Check

We can't find m and n on their own: many pairs work.

Let's check with one pair.

We pick m = 1, so that n is a small whole number.

With n = 1, 4m + 6n is 4 × 1 + 6 × 1 = 4 + 6 = 10.

It fits the question.

m = 1, n = 1: 4 × 1 + 6 × 1 = 4 + 6 = 10

And 2m + 3n is 2 × 1 + 3 × 1 = 2 + 3 = 5.

The same answer.

It works!

2m + 3n = 2 × 1 + 3 × 1 = 2 + 3 = 5

Let's look back.

First: compare the two.

Then: take out the 2.

Then: remove the 2.

Last: check.

Answer