# In a bag of coloured cubes, the ratio of red cubes to total number of cubes is 5:7. If there are 105 cubes in a bag, how many cubes are red?

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The problem provides the total number of cubes and the ratio of red cubes to total number of cubes. You can put the unknown number of red cubes equal to n, hence, you can establish the following relation between the ratios of red cubes and total number of cubes, such that:

`n/105 = 5/7`

Performing the cross multiplication yields:

`5*105 = 7n => n = 5*105/7`

Reducing like factors yields:

`n = 5*15 => n = 75 ` red cubes

**Hence, evaluating the number of red cubes yields that there exists 75 red cubes in the bag.**

In a bag of coloured cubes, the ratio of red cubes to total number of cubes is 5:7. If there are 105 cubes in a bag, how many cubes are red?

You can set up proportions to solve this.

The ratio of red cubes to total cubes is 5:7.

`(5)/(7) = (x)/(105)`

`105xx5 = 7x`

`x = (105xx5)/7`

`x = 75`

Given that : Ratio of red cubes to total number of cubes is = 5:7

and Total Number of cubes in bag = 105

`rArr` Number of Red Cubes/Total Number of Cubes = 5/7

n / 105 = 5/7

Performing Cross Multiplication

7 x n= 105 x 5

n = 525 / 7

n = 75

There are 75 Red cubes in the bag.