A factory makes 750 cakes everyday.
The cakes are ornage cakes or lemon cakes.
Each day Aadil takes a sample of 25 cakes to check.
The proportion of his cakes in his sample that are orange is the same as the proportion of the cakes made that day are orange.
On Monday, Aadil calculated that he needed exactly 7 orange cakes in his sample. What is the total number of orange cakes that were made on Monday?
Let's represent the total number of orange cakes made on Monday as "x".
The proportion of orange cakes in the sample is 7/25.
According to the information given, this proportion is the same as the proportion of orange cakes made that day, which is x/750.
Setting up the equation:
7/25 = x/750
Cross-multiplying:
7 * 750 = 25 * x
5250 = 25x
Dividing both sides by 25:
x = 5250/25
x = 210
Therefore, the total number of orange cakes made on Monday is 210.
Based on the information given, we know that Aadil takes a sample of 25 cakes each day to check the proportion of orange cakes. On Monday, Aadil calculated that he needed exactly 7 orange cakes in his sample.
Let's use algebra to solve this problem:
Let O be the number of orange cakes made on Monday.
Let T be the total number of cakes made on Monday.
Therefore, the proportion of orange cakes in Aadil's sample is 7/25.
According to the given information, the proportion of orange cakes in his sample is the same as the proportion of orange cakes made that day, so:
(O / T) = (7 / 25)
To find O, we need to calculate the value of T.
We know that the factory makes 750 cakes every day, so T = 750.
Now we can plug in the values:
(O / 750) = (7 / 25)
To solve for O, we can cross-multiply:
25O = 7 * 750
25O = 5250
Divide both sides of the equation by 25 to isolate O:
O = 5250 / 25
O = 210
Hence, the total number of orange cakes made on Monday is 210.
To find the total number of orange cakes made on Monday, we need to determine the proportion of orange cakes in Aadil's sample and then use that proportion to calculate the total number of orange cakes made.
We know that Aadil's sample consists of 25 cakes, and he calculated that he needed exactly 7 orange cakes in his sample. Therefore, the proportion of orange cakes in his sample can be calculated as:
(proportion of orange cakes in sample) = (number of orange cakes in sample) / (total sample size)
= 7 / 25
To find the total number of orange cakes made on Monday, we can apply this proportion to the total number of cakes made that day. Based on the information given, the factory makes 750 cakes each day. Therefore:
(total number of orange cakes made on Monday) = (proportion of orange cakes in sample) * (total number of cakes made)
= (7 / 25) * 750
Now, we can calculate the total number of orange cakes made on Monday:
(total number of orange cakes made on Monday) = (7 / 25) * 750
= 210
So, the total number of orange cakes made on Monday is 210.