RATIOS
To answer the question in general terms we need to look at the tools we use, the bar diagrams.
If we are given two or more different types of objects (and objects can be people) and we’re told in what ratio these types are mixed and/or how many objects there are altogether, we represent the ratios and the totals using bars split into equal sized boxes. All the boxes are the same size but the bars may have different lengths. Let’s take the ratio 3:4:5, we would have three bars, one three boxes long, another four boxes long and another five boxes long. It helps if the bars are given different colours. Let’s make the 3-box bar red, the 4-box bar yellow and the 5-box bar blue.
Then we take the bars and arrange them into a line to make a single multicoloured bar. The length of that long bar will be a total of some sort. The boxes divide the long bar into equal sections. Because we know the total length of the bar as a number, we can work out the length of each box by dividing the total by the number of boxes. And we can also work out from knowing how many boxes are red, yellow or blue, what the lengths of the red, yellow and blue bars are. So the ratios are now actual numbers of objects.
That’s the way the bar diagram works.
EXAMPLE
Let’s say we have three types of vehicle: cars, motorbikes and trucks in a parking lot. There are 510 vehicles in the parking lot, and the ratio is trucks:bikes:cars=3:4:10. The trucks are represented by the red bar, the bikes by the yellow bar, and the cars by the blue bar. The long bar is 17 boxes long so each box is 30 vehicles long because 510/17=30. Therefore there are 3×30=90 trucks, 4×30=120 bikes, 10×30=300 cars.