Peter, Bridget and Caroline share some sweets in the ratio 6:3:2. Peter gets 56 more sweets than Caroline. How many sweets are there altogether?

The scale in the ratio given considers the case that there are 9 sweets (2 + 3 + 4), however, to answer our question, we need to scale up the ratio, so that we can work out the share when we have 36 sweets

Step-by-step explanation:

Ratios are a way of displaying the proportional split of a value and they are very similar to fractions. In the example above, we see that for every 2 sweets Amy has, Beth gets 3 and, Colin will get 4. Like fractions, this proportion will stay the same regardless of the scale of the ratio. The scale in the ratio given considers the case that there are 9 sweets (2 + 3 + 4), however, to answer our question, we need to scale up the ratio, so that we can work out the share when we have 36 sweets. So, what scale factor do we need to get it from a total of 9 sweets to a sum of 36 sweets? We know that 9 multiplied by 4 gives us 36, therefore, we can use a scale factor of 4. Remember how whatever is done to the denominator of a fraction has to be done to the numerator? Ratios like to behave the same way, so now that we have scaled up the sum of the ratio, we need to scale up the individual values by 4 – (2x4) : 3x4 : 4x4. Once we work it out we get the new ratio 8:12:16. You can check if you’re right by adding up the new values and you will see that 8 + 12 + 16 = 36, which is the value that the 9 was initially scaled up to. So we now know that when sharing the 36 sweets, Amy will get 8 sweets, Beth will get 12 sweets and Colin will get 16.