A 250ml glass of cordial is made by mixing 4 parts water to 1 part syrup
Person "A" Drinks 50ml of the cordial. Person "A" thinks it is too strong and filles the glass back up by 50ml of water
i> How Much Syrup Is left
ii> What fraction of the cordial is syrup
B) Person "A" repeats this process once more
i> How Much Syrup Is left
ii>What fraction of the cordial is syrup
initially 1/5 syrup (1 syrup to 4 water) ... 50 mL syrup
i) A drinks 1/5 of the cordial (and 1/5 of the syrup) ... leaving 40 mL syrup
ii) 40 mL syrup in 250 mL cordial ... 4/25
B) i) A drinks 1/5 of the cordial (and 1/5 of the syrup) ... leaving 32 mL syrup
ii) 32 mL syrup in 250 mL cordial ... 16/125
i> To find out how much syrup is left, we need to determine the initial amount of syrup in the 250ml glass of cordial and subtract the amount of syrup that Person "A" drank.
The 250ml glass of cordial is made by mixing 4 parts water to 1 part syrup, which means that the total number of parts in the cordial mixture is 4 + 1 = 5.
To find the amount of syrup in the cordial, we divide the total volume (250ml) by the number of parts in the mixture:
Amount of syrup = (1 part / 5 parts) * 250ml = 50ml
Since Person "A" drank 50ml of the cordial, there is 50ml - 50ml = 0ml of syrup left.
ii> The fraction of the cordial that is syrup can be calculated by dividing the amount of syrup by the total volume of the cordial:
Fraction of syrup = Amount of syrup / Total volume of cordial = 50ml / 250ml = 1/5
Therefore, initially, the fraction of the cordial that is syrup is 1/5.
B) Person "A" repeats this process once more.
i> Similar to the calculation before, we need to determine the new amount of syrup after Person "A" filled the glass back up with 50ml of water.
Since Person "A" added 50ml of water, the total volume of the cordial becomes 250ml + 50ml = 300ml.
To find the new amount of syrup, we divide the initial amount of syrup (which is 0ml) by the total volume of the cordial:
Amount of syrup = (0ml / 300ml) * 300ml = 0ml
So, after Person "A" repeats the process, there is no syrup left in the cordial (i.e., 0ml of syrup).
ii> The fraction of the cordial that is syrup remains the same, as the amount of syrup is now 0ml.
Therefore, after Person "A" repeats the process, the fraction of the cordial that is syrup is still 0/300, which simplifies to 0.
To find the answers, we need to determine the initial amount of syrup in the glass and then calculate the changes that occur when water is added.
Given that the 250ml glass of cordial is made by mixing 4 parts water to 1 part syrup, we can determine the initial amounts of water and syrup in the glass.
1) Initial Amounts:
- Water: 4 parts of water to 1 part of syrup, which means the glass initially contains 4/5 * 250ml = 200ml of water.
- Syrup: 1 part of syrup, which means the glass initially contains 1/5 * 250ml = 50ml of syrup.
Now let's calculate the changes that occur when Person "A" drinks 50ml of the cordial and fills the glass back up with 50ml of water.
i) How much syrup is left after Person "A" drinks 50ml of cordial?
- Person "A" drinks 50ml of cordial, which consists of water and syrup in the same ratio as before (4 parts water to 1 part syrup).
- Since Person "A" drinks 50ml out of the initial 250ml glass, only 200ml of the mixture are left.
- The amount of water left is reduced in the same proportion as the amount of syrup, so the ratio remains 4 parts water to 1 part syrup.
- As for the remaining water, 200ml * (4/5) = 160ml remains.
- Now, the remaining amount of syrup can be calculated: 200ml - 160ml = 40ml.
- Therefore, after Person "A" drinks 50ml of the cordial, 40ml of syrup is left in the glass.
ii) What fraction of the cordial is syrup?
- The initial glass of cordial contained 200ml of water and 50ml of syrup.
- So, the initial ratio of water to syrup is 200ml : 50ml, which simplifies to 4:1.
- The fraction of syrup in the cordial can be represented as 1/(4+1) = 1/5. Therefore, 1/5 of the cordial is syrup.
Now let's repeat the process with Person "A" filling the glass again with 50ml of water.
i) How much syrup is left after Person "A" fills the glass up with 50ml of water?
- After the first round, the glass contains 200ml of water and 40ml of syrup.
- Person "A" adds 50ml of water, so the total amount of water becomes 200ml + 50ml = 250ml.
- Since the ratio of water and syrup remains the same (4:1), the ratio of water to syrup is still 4 parts water to 1 part syrup.
- The remaining water now becomes 250ml * (4/5) = 200ml.
- Therefore, after Person "A" refills the glass with 50ml of water, the amount of syrup remains the same at 40ml.
ii) What fraction of the cordial is syrup?
- After the refill, the glass contains 200ml of water and 40ml of syrup.
- The ratio of water to syrup is 200ml : 40ml, which also simplifies to 4:1, just like before.
- So, the fraction of syrup in the cordial remains 1/5.
In summary:
A) After Person "A" drinks 50ml of the cordial and refills the glass with 50ml of water:
i) There will be 40ml of syrup left in the glass.
ii) One-fifth (1/5) of the cordial is syrup.
B) After Person "A" repeats the process and adds an additional 50ml of water:
i) The amount of syrup left remains at 40ml.
ii) Still, one-fifth (1/5) of the cordial is syrup.