a factory can produce 45 containers of yogurt in t minutes, 950 grams of fruit are used for every 25 containers of yogurt
b) find in terms of t the time taken by the factory to produce 100 containers of yogurt
c) if t=6 find the amount of fruit used in producing containers of yogurt in 8 minutes
3.250kilogram
a) 225/t containers
b) 20t/9 minutes
c) 2,280 grams
b) To find the time taken by the factory to produce 100 containers of yogurt, we can set up a proportion.
The factory can produce 45 containers of yogurt in t minutes.
Therefore, in 1 minute, the factory can produce 45/t containers of yogurt.
Using this information, we can set up the proportion:
45/t = 100/x
Here, x is the time taken to produce 100 containers of yogurt.
To solve for x, we can cross-multiply and solve for x:
45x = 100t
Divide both sides of the equation by 45:
x = (100t)/45
Therefore, the time taken by the factory to produce 100 containers of yogurt in terms of t is (100t)/45.
c) If t = 6, we can find the amount of fruit used in producing containers of yogurt in 8 minutes.
We know that 950 grams of fruit are used for every 25 containers of yogurt.
So, in 1 container of yogurt, the factory uses (950 grams) / (25 containers) = 38 grams of fruit.
To find the amount of fruit used in 8 minutes, we can set up a proportion:
1/t = 8/8
Using this proportion, we can conclude that in 8 minutes, the factory produces 8 times the number of containers of yogurt compared to 1 minute.
Therefore, in 8 minutes, the factory produces 8 * (45/t) containers of yogurt.
And the amount of fruit used in 8 minutes is (8 * (45/t)) * (38 grams) = (360 * 38) / t = (13680/t) grams of fruit.
If t = 6, then the amount of fruit used in producing containers of yogurt in 8 minutes is (13680/6) = 2280 grams.
To solve these problems, we need to use the given information and apply some mathematical calculations. Let's break down each question step by step:
b) To find the time taken by the factory to produce 100 containers of yogurt in terms of t, we can set up a proportion using the information given.
We know that the factory can produce 45 containers of yogurt in t minutes. So, the rate of production is 45 containers/t minutes.
To find the time taken to produce 100 containers, we can set up a proportion:
45 containers / t minutes = 100 containers / x minutes
Cross-multiply and solve for x:
45x = 100t
Divide both sides by 45:
x = (100t) / 45
Therefore, the time taken by the factory to produce 100 containers of yogurt in terms of t is (100t) / 45.
c) If t = 6, we can find the amount of fruit used in producing containers of yogurt in 8 minutes.
We know that 950 grams of fruit are used for every 25 containers of yogurt.
First, let's find the ratio of fruit used to containers of yogurt:
950 grams / 25 containers
To find the amount of fruit used in 8 minutes, we can set up a proportion:
950 grams / 25 containers = x grams / 8 minutes
Cross-multiply and solve for x:
(950 * 8) = 25x
7600 = 25x
Divide both sides by 25:
x = 304 grams
Therefore, if t = 6, the amount of fruit used in producing containers of yogurt in 8 minutes is 304 grams.