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
b. Time = (100/45) * t = 2.22t.
c. (45/6min) * 8min = 60 Containers.
Amt.=(950grams/25cont. * 60=2280 Grams
b) To find the time taken by the factory to produce 100 containers of yogurt, we need to determine how many containers can be produced in 1 minute, and then use that information to find the time for 100 containers.
In 1 minute, the factory can produce 45/t containers of yogurt.
Therefore, the time taken to produce 100 containers is:
100 containers * (t minutes / 45 containers) = (100t) / 45 minutes
c) If t = 6, we can find the amount of fruit used in producing containers of yogurt in 8 minutes.
In 8 minutes, the number of containers produced would be:
8 minutes * (45 containers / t minutes) = 8 * 45 / 6 = 60 containers
Since 950 grams of fruit are used for every 25 containers of yogurt:
Amount of fruit used = (950 grams / 25 containers) * 60 containers = 2280 grams of fruit.
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 given information.
Given:
45 containers of yogurt can be produced in t minutes
Let's set up the proportion:
45 containers of yogurt / t minutes = 100 containers of yogurt / x minutes
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, in terms of t, the time taken by the factory to produce 100 containers of yogurt is (100t) / 45 minutes.
For part c, where t = 6:
To find the amount of fruit used in producing 8 containers of yogurt in 6 minutes, we can set up a proportion using the given information:
Given:
950 grams of fruit are used for every 25 containers of yogurt
Let's set up the proportion:
950 grams of fruit / 25 containers of yogurt = x grams of fruit / 8 containers of yogurt
To solve for x, we can cross-multiply and solve for x:
950 * 8 = 25x
Divide both sides of the equation by 25:
x = (950 * 8) / 25
Calculating the value:
x = 304 grams
Therefore, when t = 6, the amount of fruit used in producing 8 containers of yogurt in 6 minutes is 304 grams.