Gloves are sold in size small, medium, or large. When a clothing shop places an order for gloves, the number of small, medium, and large gloves that they order are in the ratio four to 12 to nine. What percentage of the gloves that they order are large?
We’ve been told in the question that the ratio of small to medium to large gloves is four to 12 to nine. The numbers in this ratio are in the same order as the sizes are given in the question. So that’s four parts small gloves, 12 parts medium gloves, and nine parts large gloves.
We’ve been asked to find the percentage of the gloves that they order, which are large. And we can first work out the fraction or the proportion of the gloves that they order, which are large. We know that nine parts of the ratio are large gloves. The total number of parts in this ratio is four plus 12 plus nine which is equal to 25.
So the number of large gloves is represented by nine parts out of 25. And remember in a ratio all of the parts are of equal size. We can write nine out of 25 as the fraction nine over 25 or nine twenty-fifths.
Remember though that we were asked to give our answer as a percentage. And percent literally means out of 100. So to convert this fraction into a percentage, we can first find an equivalent fraction where the denominator is 100.
To scale 25 up to 100, we have to multiply by four as 25 times four is 100. So in order for this fraction to be equivalent, we must also do the same to the numerator. Nine multiplied by four is 36. So the fraction of large gloves is 36 over 100. 36 over 100 or 36 per 100 is 36 percent.
So the percentage of the gloves that the clothing shop order which were large is 36 percent.