The total number of sicience books were 196.
What is ratio?
Ratio is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division.
Let the total numbers of science books be x and maths books be y.
According to the given question.
The intial ratio of maths books to the science books is 3:7.
⇒ [tex]\frac{y}{x} = \frac{3}{7}[/tex] ...(i)
But, after the addition of 84 maths books the ratio gets changed to 6:7.
[tex]\implies \frac{y +84}{x} = \frac{6}{7}[/tex] ...(ii)
Solving the equations i and ii.
From equation i.
[tex]7y = 3x[/tex]
And from equation ii
[tex]7y + 7(84) = 6x[/tex]
Substitute the value of 7y = 3x in the above equation.
[tex]3x + 588 = 6x[/tex]
[tex]\implies 588 = 6x -3x[/tex]
[tex]\implies 3x = 588[/tex]
[tex]\implies x = \frac{588}{3}[/tex]
[tex]\implies x = 196[/tex]
Hence, the total number of sicience books were 196.
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