Two cousins were born eight years apart. How old will the elder be when the sum of their ages is equal to 20 years?
So when we look at this question, the first thing to consider is the two cousins were born eight years apart. So to help us solve this problem, what I’m gonna is I’m actually gonna say that the younger cousin is gonna be denoted by 𝑥. And so therefore, the elder cousin we can consider being 𝑥 plus eight and that’s because they were born eight years apart. So we know that actually the elder cousin is going to be eight years older than the younger cousin.
Okay, great! So we now here we got expressions for each of the cousins. Next piece of information that the question actually gives us is that the sum of the cousins’s ages is equal to 20 years. So it’s fantastic cause we can actually use this now to form an equation. So we can say that 𝑥 plus 𝑥 plus eight is equal to 20. That’s because we get 𝑥 first of all because that’s the younger cousin’s age plus 𝑥 plus eight because that’s the elder cousin’s age. And that’s all equal to 20 because that we said the sum of their ages is equal to 20.
Great! So now what we need to do is actually collect terms and start solving this. So if we collect like terms, we get two 𝑥 plus eight is equal to 20. Then, next, we subtract eight from each side, which gives us two 𝑥 is equal to 12. And then, we divide each side by two. And we find out that 𝑥 is equal to six.
Okay, great! Is that has finished? Well, no because the question is actually asking us to find out how old the elder cousin will be. And what we found out is actually 𝑥, which is the age of the younger cousin. Okay, so let’s move on to the final part of the question.
So we’re gonna substitute 𝑥 equals six into 𝑥 plus eight because that’s the expression for the elder cousin’s age. So this is gonna give us six plus eight, which is equal to 14. So therefore, we can say that the elder cousin is 14 years old.
And we can quickly check this because if we take the young cousin’s age, which is six, and we add it to the older cousin’s age, which is 14, then we get the answer of 20, which is great because 20 years is the sum of their ages.