Video: AQA GCSE Mathematics Foundation Tier Pack 1 • Paper 3 • Question 11

Pip goes to visit her cousin. The sum of Pip’s age and her cousin’s age is 26. Four years ago, Pip was half her cousin’s age. How old is Pip now?

03:06

Video Transcript

Pip goes to visit her cousin. The sum of Pip’s age and her cousin’s age is 26. Four years ago, Pip was half her cousin’s age. How old is Pip now?

Since we’re solving for Pip’s age, let’s go ahead and let 𝑃 represent Pip’s age and 𝐶 stand for her cousin’s age. So let’s go through what we’re given. Pip goes to visit her cousin and the sum of Pip’s age and her cousin’s age is 26. So we have that the sum of Pip’s age and her cousin’s age is 26.

So from the word “sum,” we know that we’re adding and it’s the sum of Pip’s age and her cousin’s age. And we know that this is, so equals, 26. So that will be one equation that we can use. Now, let’s use the next sentence to create another equation.

Four years ago, Pip was half her cousin’s age. So first of all, how do we represent four years ago? Well, we would need to take Pip’s age and subtract four and her cousin’s age and subtract four. So four years ago, Pip was half of her cousin’s age. So Pip then — represented by 𝑃 minus four — was equal to half of her cousin’s age, which would have been 𝐶 minus four.

While we could use this equation, sometimes it’s not very fun to work with fractions. So let’s go ahead and multiply both sides of this equation by two to get rid of the fraction. So we have two times 𝑃 minus four is equal to 𝐶 minus four.

Now, using these two equations, we can figure out how old Pip is now. So here are the two equations that we’ve created: 𝑃 plus 𝐶 is equal to 26 and two times 𝑃 minus four is equal to 𝐶 minus four. So we need to essentially solve for 𝑃. Well, using this first equation, we know that 𝑃 is equal to 26 minus 𝐶 from subtracting 𝐶 from both sides of the equation.

Now while this doesn’t give us our answer, we could replace 𝑃 with 26 minus 𝐶 into this second equation. And then the second equation will only be in terms of 𝐶. And then we can solve for 𝐶, plug it back into this equation of 𝑃 equals 26 minus 𝐶, and solve for 𝑃. So here, we’ve replaced 𝑃 with 26 minus 𝐶.

Now, we can combine 26 and negative four which is 22. And now, we need to expand two. Two times 22 is 44 and two times negative 𝐶 is negative two 𝐶. So let’s solve for 𝐶. Let’s go ahead and add two 𝐶 to both sides of the equation. And we have that 44 is equal to three 𝐶 minus four. Adding four to both sides of the equation, we get that 48 is equal to three 𝐶. And after dividing both sides of the equation by three, we find that 𝐶 is equal to 16.

So her cousin’s age is 16. Now to solve for 𝑃, we can take 16 and plug it in for 𝐶. And 26 minus 16 gives us 10. So this means Pip’s age is 10.

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