A jumper manufacturer has blue, grey, and orange lengths of wool in the ratio blue to grey to orange equals 12 to 21 to five. There are 8592 more meters of grey wool than meters of orange wool. Work out the length of the blue wool.
We’ve been given the ratio of blue to grey to orange lengths of wool. This tells us how much the jumper manufacturer has of each color of wool relative to the other lengths. We’re also told that there are 8592 more meters of grey wool than meters of orange wool. In the ratio, we see that there are 21 parts grey wool and five parts orange wool. We can work out the difference in the number of parts of grey and orange wool by subtracting five from 21, which is equal to 16. As there are 8592 more meters of grey wool than orange and 16 parts more grey wool than orange, this means that those 16 parts represent 8592 meters.
We can use this information to work out how many meters a single part of the ratio is equal to. To scale down from 16 parts to one part, we have to divide by 16. So we need to do the same thing for the number of meters. 8592 divided by 16 is equal to 537. So each part in this ratio represents 537 meters. The question asked us to work out the length of the blue wool. And looking back at the ratio, we can see that the blue wool is represented by 12 parts. So we can take the length that we’ve just found for one part and multiply it by 12. 12 multiplied by 537 is 6444. So the length of blue wool that the jumper manufacturer has is 6444 meters.
Now we could actually have done the scaling from 16 parts to 12 parts slightly differently if we wanted, as they have common factors that are higher than one. One alternative method would be to find the value of four parts. So we could divide 16 by four and also divide 8592 by four to show that four parts is equivalent to 2148 meters. To scale up from four parts to 12 parts, we’d need to multiply by three. And multiplying 2148 by three does give 6444 as before. So this would be an alternative way of doing the scaling. We could also have chosen to scale down from 16 parts to two parts by dividing by eight and then up to 12 parts by multiplying by six. But in any case, it would give us the same answer.