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Answer :
Sure! Let's take a look at each part of the question step-by-step:
(i) How many cans of food will be needed to feed 12 cats in a week?
1. We know that 3 cans are used to feed 4 cats in one day. First, calculate how many cans are needed for one cat in one day:
- Since 3 cans feed 4 cats in one day, this means [tex]\( \frac{3}{4} \)[/tex] cans are needed per cat per day.
2. Next, determine the number of cans needed to feed one cat for a whole week (7 days):
- Multiply the daily requirement by 7 (days in a week): [tex]\( \frac{3}{4} \times 7 = \frac{21}{4} \)[/tex].
3. Now, calculate how many cans are needed for 12 cats in a week:
- Multiply the weekly requirement per cat by the number of cats: [tex]\( \frac{21}{4} \times 12 = 63 \)[/tex].
So, a total of 63 cans are needed to feed 12 cats in a week.
(ii) How many cats can be fed for 12 days on 72 cans of cat food?
1. We know from before that one cat needs [tex]\( \frac{3}{4} \)[/tex] cans per day.
2. First, calculate the total amount of cans needed for one cat over 12 days:
- Multiply the daily requirement by the number of days: [tex]\( \frac{3}{4} \times 12 = 9 \)[/tex].
3. Now, determine how many cats can be fed if you have 72 cans for these 12 days:
- Divide the total available cans by the cans required per cat for 12 days: [tex]\( \frac{72}{9} = 8 \)[/tex].
Thus, 72 cans can feed 8 cats for 12 days.
(iii) For how many days will 36 cans of food feed 6 cats?
1. Again, we know that [tex]\( \frac{3}{4} \)[/tex] cans are required per cat per day.
2. Calculate how many cans are needed for 6 cats for one day:
- Multiply the single cat requirement by 6: [tex]\( \frac{3}{4} \times 6 = 4.5 \)[/tex].
3. Finally, calculate how many days 36 cans will last for these 6 cats:
- Divide the total available cans by the daily requirement for 6 cats: [tex]\( \frac{36}{4.5} = 8 \)[/tex].
Therefore, 36 cans of food will feed 6 cats for 8 days.
I hope this helps you understand the solution! If you have any more questions, feel free to ask.
(i) How many cans of food will be needed to feed 12 cats in a week?
1. We know that 3 cans are used to feed 4 cats in one day. First, calculate how many cans are needed for one cat in one day:
- Since 3 cans feed 4 cats in one day, this means [tex]\( \frac{3}{4} \)[/tex] cans are needed per cat per day.
2. Next, determine the number of cans needed to feed one cat for a whole week (7 days):
- Multiply the daily requirement by 7 (days in a week): [tex]\( \frac{3}{4} \times 7 = \frac{21}{4} \)[/tex].
3. Now, calculate how many cans are needed for 12 cats in a week:
- Multiply the weekly requirement per cat by the number of cats: [tex]\( \frac{21}{4} \times 12 = 63 \)[/tex].
So, a total of 63 cans are needed to feed 12 cats in a week.
(ii) How many cats can be fed for 12 days on 72 cans of cat food?
1. We know from before that one cat needs [tex]\( \frac{3}{4} \)[/tex] cans per day.
2. First, calculate the total amount of cans needed for one cat over 12 days:
- Multiply the daily requirement by the number of days: [tex]\( \frac{3}{4} \times 12 = 9 \)[/tex].
3. Now, determine how many cats can be fed if you have 72 cans for these 12 days:
- Divide the total available cans by the cans required per cat for 12 days: [tex]\( \frac{72}{9} = 8 \)[/tex].
Thus, 72 cans can feed 8 cats for 12 days.
(iii) For how many days will 36 cans of food feed 6 cats?
1. Again, we know that [tex]\( \frac{3}{4} \)[/tex] cans are required per cat per day.
2. Calculate how many cans are needed for 6 cats for one day:
- Multiply the single cat requirement by 6: [tex]\( \frac{3}{4} \times 6 = 4.5 \)[/tex].
3. Finally, calculate how many days 36 cans will last for these 6 cats:
- Divide the total available cans by the daily requirement for 6 cats: [tex]\( \frac{36}{4.5} = 8 \)[/tex].
Therefore, 36 cans of food will feed 6 cats for 8 days.
I hope this helps you understand the solution! If you have any more questions, feel free to ask.
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