The total number of yellow marbles in the bag was 78 marbles
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
Given data ,
The ratio of yellow marbles to purple marbles in the bag = 13 : 4
Let the total number of yellow marbles in the bag be = 13x
Let the total number of purple marbles in the bag be = 4x
Now , the equation will be
The total number of marbles in the bag = 102
So , substituting the values in the equation , we get
The total number of marbles in the bag = total number of yellow marbles + total number of purple marbles
The total number of marbles in the bag = 13x + 4x
13x + 4x = 102
17x = 102
Divide by 17 on both sides of the equation , we get
x = 6
Therefore , substituting the value of x in the above expressions , we get
Total number of yellow marbles in the bag = 13x
Total number of yellow marbles in the bag = 13 x 6
Total number of yellow marbles in the bag = 78 marbles
And ,
Total number of purple marbles in the bag = 4x
Total number of purple marbles in the bag = 4 x 6
Total number of purple marbles in the bag = 24 marbles
Hence , The total number of yellow marbles in the bag was 78 marbles
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