Rosie and Jack are playing a computer game. Their combined score is 1574. Jack scored 64 points less than Rosie. How many points did Rosie score?
So in order to actually help us work this out, what I’m gonna say is I’m gonna call Rosie’s score 𝑅 and Jack’s score 𝐽. Well, using these letters, we can actually start to form a couple of equations, the first of which being 𝑅 plus 𝐽, so Rosie’s score plus Jack’s score, is equal to 1574, because we’re told in the question that their combined score is 1574. The second equation we can set up is 𝐽, so Jack’s score, is equal to 𝑅, Rosie’s score, minus 64. And that’s because, in the question, we’re told that Jack scored 64 points less than Rosie.
Now if we take a look at the two equations, we can see that actually, in the second equation, we’re told what 𝐽 is in terms of 𝑅. So 𝐽 is equal to 𝑅 minus 64. We’ve also got a 𝐽 in the first equation. So therefore, what we can do — well, I’ve actually labeled our equations one and two — is we can substitute equation two into equation one, because we know what 𝐽 is in terms of 𝑅 and we can actually substitute this in in place of the 𝐽 in our first equation.
So when we do that, we get 𝑅 plus 𝑅 minus 64 — that’s because 𝐽 was equal to 𝑅 minus 64, so we’ve substituted that in — is equal to 1574. And the reason we’ve done this is that actually all we’ve got is actually an equation in terms of 𝑅, because we want to find out 𝑅 because that’s Rosie’s score.
So now what we need to do is solve this equation to find 𝑅, Rosie’s score. So the first step is to actually combine our like terms. So we’re gonna collect 𝑅 plus 𝑅, which is gonna give us two 𝑅. Then we’ve got two 𝑅 minus 64 is equal to 1574. So then the next step is to actually add 64 to both sides of the equation. And we do that so that we’re actually left with two 𝑅 on the left-hand side, because negative 64 add 64 is zero. And remember in whatever we do to one side of the equation we must do to the other side of the equation. So this is gonna give us two 𝑅 is equal to 1638.
So then the next step is to actually divide each side of the equation by two. And that’s because we know that two 𝑅 is equal to 1638, but we want just one 𝑅, because we want Rosie’s score. So we divide each side of the equation by two, and we get 𝑅 is equal to 819.
So therefore, we can say that if Rosie and Jack are playing a computer game and their combined score is 1574 and Jack scored 64 points less than Rosie, then Rosie scored 819 points. And we can actually double check this to make sure we got the right answer, because what we can do is work out Jack’s score, cause Jack’s score is going to be 64 less than 819, so it’s 819 minus 64, which is gonna be 755. So therefore, if we add Rosie’s and Jack’s score, we’re gonna have 819, which is Rosie’s score, plus 755, which is Jack’s score, which gives us 1574, which is the combined score that we’ve been told in the question. So therefore, we can say yes, definitely, Rosie’s score was 819.