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3.3 G) Told the Difference
3.3 G) Told the Difference
In the exam, you may be given a ratio and told the difference between the amounts that the different components of the ratio represent. Based on this information, you could be asked to either work out how much each part of the ratio represents or the total amount that has been shared out.
This will all make much more sense when we look through a few examples.
This will all make much more sense when we look through a few examples.
Example 1
I have a bracelet that contains pink and green stones. The ratio of pink stones to green stones in the bracelet is 5 : 2. There are 15 more pink stones than green stones. How many pink stones are there and how many green stones are there?
I have a bracelet that contains pink and green stones. The ratio of pink stones to green stones in the bracelet is 5 : 2. There are 15 more pink stones than green stones. How many pink stones are there and how many green stones are there?
We are told the ratio between the pink and green stones, which is 5 : 2. We are also told that there are 15 more pink stones than there are green stones. In the ratio, we see that there are 5 parts that are pink and 2 parts that are green. From this information, we can see that the difference between the two components of the ratio is 3 parts (5 – 2) and these 3 parts represents the difference between the two stones, which is 15. Therefore, 3 parts of the ratio represents 15 stones. We are now able to work out what 1 part of the ratio represent by dividing 15 by 3. This tells us that 1 part of the ratio is 5 stones.
The next step is to multiply the number of parts that are pink and green by the number of stones per part (5).
Therefore, there are 25 pink stones and 10 green stones.
- Pink – 5 x 5 = 25 stones
- Green – 2 x 5 = 10 stones
Therefore, there are 25 pink stones and 10 green stones.
Example 2
I am making orange and pineapple juice. The ratio of oranges to pineapples is 7 : 3. To make my desired quantity of orange and pineapple juice, I am using 28 more oranges than pineapples. How many oranges am I using and how many pineapples am I using?
I am making orange and pineapple juice. The ratio of oranges to pineapples is 7 : 3. To make my desired quantity of orange and pineapple juice, I am using 28 more oranges than pineapples. How many oranges am I using and how many pineapples am I using?
This question tells us that we are using 28 more oranges than pineapples. The question gives us the ratio of oranges to pineapples (7 : 3) and from the ratio, we can see that oranges have 4 more parts than pineapples (oranges have 7 parts and pineapples have 3 parts, so the difference is 4 parts; 7 – 3 = 4). We now know that 4 parts of the ratio represent 28 and from this information we can find what 1 part represents by dividing 28 by 4. This tells us that 1 part is equal to 7.
The next step is to find how many oranges and pineapples we are using by multiplying the number of parts by the amount that 1 part equals (7).
Therefore, we use 49 oranges and 21 pineapples to make our juice.
- Oranges – 7 x 7 = 49
- Pineapple – 3 x 7 = 21
Therefore, we use 49 oranges and 21 pineapples to make our juice.