Video: Pack 2 • Paper 3 • Question 13

Pack 2 • Paper 3 • Question 13

02:50

Video Transcript

Three babies are playing with a set of building blocks. Alfie has some number of blocks. Bertie has four times as many blocks as Alfie. Cara has three less blocks than Bertie. The babies have a total of 51 blocks. One of the parents says, “If Cara gives some blocks to Alfie, then Cara and Alfie will have the same number of blocks.” Is this statement correct? You must show your reasoning.

Let’s start by defining the number of blocks that Alfie has. Since we don’t know exactly how many blocks that is, we can give it a letter. Let’s call it 𝑎, where 𝑎 is an integer or a whole number.

Remember since 𝑎 is the number of blocks that Alfie has, it simply has to be a whole number since we can’t split these blocks into pieces. This means then that Bertie has four 𝑎 blocks since four 𝑎 means four times 𝑎 and we’re told that he has four times as many blocks as Alfie.

We’re told that Cara has three less blocks than Bertie. And we’ve just stated that Bertie has four 𝑎 blocks. So Cara must have four 𝑎 minus three blocks.

We’re also told that the total number of blocks is 51. So we can add together each of our expressions and form an equation by making the total equal to 51. That’s 𝑎 plus four 𝑎 plus four 𝑎 minus three equals 51. Next, we should simplify by collecting like terms. 𝑎 plus four 𝑎 plus four 𝑎 is nine 𝑎. So our equation is nine 𝑎 minus three equals 51.

Next, we’ll solve this equation by applying the inverse operations. First, to get rid of the minus three, we’ll add three to both sides of the equation. That gives us nine 𝑎 is equal to 54. Nine 𝑎 means nine multiplied by 𝑎. So the inverse operation here is to divide both sides by nine. That gives us that 𝑎 is equal to six.

That means Alfie has six blocks. Since Bertie has four times the number of blocks Alfie has, he must have four multiplied by six which is 24 blocks. Cara has three less than this and 24 minus three is 21. We can see then that Alfie has six blocks and Cara has 21.

Is there a way then for these two children to share their blocks so that they have the exact same number? Well, first, if we add together the total number of blocks that Alfie and Cara have, we get 21 plus six is equal to 27. 27 cannot be split between two people without splitting a block. So the parent is wrong.

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