Final answer:
To find the total number of fruits in the store, we calculate the fraction of the store that are mangoes by subtracting the sum of the fractions of other fruit types from 1 and then use the number of mangoes to set up a proportion to find the total number of fruits, which is 85.
Step-by-step explanation:
To determine the total number of fruits in the store, first, we need to find the fraction that represents the mangoes. We are given that 7/12 of the fruits are pineapples, 1/36 are oranges, and 5/24 are watermelons; adding these fractions gives us:
7/12 + 1/36 + 5/24 = 21/36 + 1/36 + 3/36 = 25/36
This means that 25/36 of the fruits are pineapples, oranges, and watermelons combined. Since the total fraction must equal 1, the fraction of the store that are mangoes can be found by subtracting from 1:
1 - 25/36 = 36/36 - 25/36 = 11/36
Now, we are given that there are 26 mangoes in the store, which equates to the 11/36 of the total fruit. To find the total number of fruits, we set up a proportion:
11/36 = 26/Total number of fruits
We can solve for the total number of fruits by cross-multiplying and dividing:
11 x Total number of fruits = 36 x 26
Total number of fruits = (36 x 26) / 11
Total number of fruits = 936 / 11
Total number of fruits = 85
Therefore, there are a total of 85 fruits in the store.