Jane was given a bag of sweets and ate two-thirds of them right away. The next day she ate two-thirds of the remainder and the following day she ate two-thirds of the remaining candy before stopping. Only 2 pieces of candy were left. How many sweets was he given in the beginning?

Respuesta :

Answer:

54

Step-by-step explanation:

First you take two and multiply it by three, which gives you 6. Then you multiply it by three and get 18. Then you multiply and get 54.

Answer:

54

Step-by-step explanation:

Let the initial amount of sweets be x

Jane ate two-thirds of them = [tex]\frac{2}{3}x[/tex]

Remaining sweets = [tex]x-\frac{2}{3}x[/tex]

                               = [tex]\frac{1}{3}x[/tex]

The next day she ate two-thirds of the remainder i.e. [tex]\frac{2}{3} \times \frac{1}{3}x =\frac{2}{9}x[/tex]

Remaining sweets = [tex]\frac{1}{3}x-\frac{2}{9}x[/tex]

                            = [tex]\frac{1}{9}x[/tex]

The following day she ate two-thirds of the remaining candy before stopping.

She ate =  [tex]\frac{2}{3} \times \frac{1}{9}x =\frac{2}{27}x[/tex]

Remaining sweets = [tex]\frac{1}{9}x-\frac{2}{27}x=\frac{1}{27}x[/tex]

Now we are given that Only 2 pieces of candy were left

So, [tex]\frac{1}{27}x=2[/tex]

[tex]x=2 \times 27[/tex]

[tex]x=54[/tex]

Hence she has given 54 sweets in the beginning.