Video: GCSE Mathematics Foundation Tier Pack 5 • Paper 1 • Question 18

GCSE Mathematics Foundation Tier Pack 5 • Paper 1 • Question 18

02:23

Video Transcript

Jill and Mick each have 𝑥 marbles. Jill gives Mick 10 of her marbles and then buys a further 𝑦 marbles. Mick then loses half of his marbles. Write expressions for the number of marbles that Jill and Mick have now.

Writing an expression means we want to represent the sentences above using algebra, so using a combination of letters and numbers. Let’s think about the number of marbles that Jill will have first.

We’re told in the beginning of the question that Jill and Mick each have 𝑥 marbles, so this is the number of marbles that Jill starts with. Next, we’re told that Jill gives Mick 10 of her marbles, so Jill will now have 10 less marbles than she started with. So we need to subtract 10 from the starting number, which gives us the expression 𝑥 minus 10. Finally, we’re told that Jill then buys a further 𝑦 marbles. So the number of marbles that she has increases by 𝑦, which means we need to add 𝑦 to our expression.

Our expression for the number of marbles that Jill has now is 𝑥 minus 10 plus 𝑦. This expression can’t be simplified as we don’t have any like terms, by which we mean terms which have the same letters.

Now let’s write down our expression for the number of marbles that Mick has. Like Jill, he starts off with 𝑥 marbles. Jill then gives Mick 10 of her marbles, which means that the number of marbles Mick has will increase by 10. So our expression is now 𝑥 plus 10. Mick then loses half of his marbles, which means he only has half of his marbles remaining. So we need to divide the number of marbles by two. We divide 𝑥 plus 10 by two by writing a fraction line and then a two in the denominator. We could also write this as a half multiplied by 𝑥 plus 10, as dividing by two is the same as multiplying by a half.

So we’ve written down our expressions for the number of marbles that Jill and Mick each have now. Jill has 𝑥 minus 10 plus 𝑦 marbles, and Mick has a half 𝑥 plus 10 marbles.

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