To find the total number of biscuits Saanvi originally made, let's follow these steps:
1. Let's denote the total number of biscuits Saanvi made as [tex]\( x \)[/tex].
2. Saanvi sold a fraction of the biscuits, specifically [tex]\(\frac{5}{13}\)[/tex] of them. This means she sold [tex]\(\frac{5}{13} \times x\)[/tex] biscuits.
3. After selling, Saanvi has 80 biscuits left. This can be expressed in an equation:
[tex]\[ x - \frac{5}{13}x = 80 \][/tex]
4. Simplify the equation by combining like terms:
[tex]\[ x \left(1 - \frac{5}{13}\right) = 80 \][/tex]
5. Calculate [tex]\(1 - \frac{5}{13}\)[/tex]:
[tex]\[ 1 - \frac{5}{13} = \frac{13}{13} - \frac{5}{13} = \frac{8}{13} \][/tex]
6. Substitute [tex]\(\frac{8}{13}\)[/tex] back into the equation:
[tex]\[ x \times \frac{8}{13} = 80 \][/tex]
7. Solve for [tex]\( x \)[/tex] by isolating the variable:
[tex]\[ x = 80 \div \frac{8}{13} \][/tex]
8. Dividing by a fraction is equivalent to multiplying by its reciprocal:
[tex]\[ x = 80 \times \frac{13}{8} \][/tex]
9. Perform the multiplication:
[tex]\[ x = 80 \times \frac{13}{8} = 130 \][/tex]
So, the total number of biscuits Saanvi originally made is 130.
