Step by step
The question
Question: if 6a + 9b = 24, what is 2a + 3b?
We want 2a + 3b.
Let's look for it inside the equation.
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Compare the two
Look at 6a + 9b and 2a + 3b.
We compare them part by part.
6 divided by 2 is 3.
So 6a is 3 times 2a.
9 divided by 3 is 3.
So 9b is 3 times 3b.
Every part of 6a + 9b is 3 times a part of 2a + 3b.
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 + 3b).
Opening the bracket gives 6a + 9b back.
3 Remove the 3
3(2a + 3b) 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.
They cancel each other.
So just the bracket is left.
24 divided by 3 is 8.
So 2a + 3b = 8!
Careful!
Both sides are divided by 3.
24 becomes 8.
The right way: 2a + 3b = 8.
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 = 2, 6a + 9b is 6 × 1 + 9 × 2 = 6 + 18 = 24.
It fits the question.
And 2a + 3b is 2 × 1 + 3 × 2 = 2 + 6 = 8.
The same answer.
It works!
5 Pick the choice
Our answer is 2a + 3b = 8.
That is choice A.
6 Why not the others
B is 12.
Wrong: 24 ÷ 2: 6a + 9b is 3 times 2a + 3b, so we divide by 3.
C is 21.
Wrong: 24 − 3: took away 3 instead of dividing by 3.
D is 72.
Wrong: 24 × 3: multiplied instead of dividing.
Let's look back.
First: compare the two.
Then: take out the 3.
Then: remove the 3.
Then: check.
Then: pick the choice.
Last: why not the others.