Saanvi makes some biscuits. She sells [tex] \frac{5}{13} [/tex] of the biscuits. She now has 80 biscuits left.

Work out the total number of biscuits Saanvi makes.



Answer :

To find the total number of biscuits Saanvi originally made, let's follow these steps: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So, the total number of biscuits Saanvi originally made is 130.