Two measurements, 𝐴 and 𝐵, are identified on a tape measure. The length between 𝐴 and 𝐵 is 35 centimeters. Calculate the values 𝐴 and 𝐵.
Well, the first thing we can see is that the length between 𝐴 and 𝐵 is 35 centimeters and what I’ve done is I’ve actually marked this onto the diagram. And if we count the number of steps between them, we can see that there’re actually five steps between 𝐴 and 𝐵. So therefore, what we can do now is actually work out the value of each of these steps.
And the value of each step is going to be 35 — because that’s the distance between 𝐴 and 𝐵 — divided by the number of steps which was five which is going to be equal to seven. So therefore, we can say that the distance between each step on our tape measure is going to be seven centimeters. And I’ve marked this on the diagram as well.
So therefore, we can actually use this to actually work out the values of 𝐴 and 𝐵. So we’re gonna start with value 𝐴. 𝐴 is gonna be equal to 50 because we’ve got 50 centimeters marked on our diagram minus two multiplied by seven. And that’s because there are two gaps — so two steps — between 𝐴 and 50 and each of these is seven centimeters. So therefore, this is going to be 50 minus 14, which is gonna give us a value of 𝐴 of 36.
Okay, great! Now, let’s move on to 𝐵. Well, the value of 𝐵, 𝐵 is going to be equal to 50 plus then three multiplied by seven. And this is because there are three steps from 50 centimeters to 𝐵 and each step is worth seven centimeters.
So we calculate 𝐵 by adding three multiplied by seven to 50. So therefore, this is going to be 50 plus 21 and that’s because three multiplied by seven is 21, which will give us an answer of 71.
So therefore, we can say that the values of 𝐴 and 𝐵 are 36 and 71, respectively.