Step by step
The question
Question: if 6a + 3b = 15, what is 2a + b?
We want 2a + b.
Let's look for it inside the equation.
1 Compare the two
Look at 6a + 3b and 2a + b.
We compare them part by part.
6 divided by 2 is 3.
So 6a is 3 times 2a.
3b is 3 times b.
Every part of 6a + 3b is 3 times a part of 2a + b.
2 Take out the 3
So we can write each part as 3 times.
3 times each part is the same as 3 times the whole bracket: 3(2a + b).
Opening the bracket gives 6a + 3b back.
3 Remove the 3
3(2a + b) means 3 times the bracket.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
So just the bracket is left.
15 divided by 3 is 5.
So 2a + b = 5!
Careful!
Both sides are divided by 3.
15 becomes 5.
4 Check
We can't find a and b on their own: many pairs work.
Let's check with one pair.
We pick a = 1, so that b is a small whole number.
With b = 3, 6a + 3b is 6 × 1 + 3 × 3 = 6 + 9 = 15.
It fits the question.
And 2a + b is 2 × 1 + 3 = 2 + 3 = 5.
The same answer.
It works!
Let's look back.
First: compare the two.
Then: take out the 3.
Then: remove the 3.
Last: check.