A publisher had a title reduction and lost 2/3 of its titles. If 52 titles were left after the reduction, how many titles were there originally?

Question

52 titles left

2/3 lost

How many originally?

Answer 1

If we know that 52 is after 2/3 of the titles were lost. Then we know that the total was 3/3. 

 

3/3(total) - 2/3(what was lost) = 1/3 which equals 52 remaining.

 

We need to now take 52 which represents 1/3 and multiply it by 3 to make the total.

 

(1/3)+(1/3)+(1/3)=(3/3)

52+52+52=156

 

3(52)=156 is the total.

 

Lets plug it back in and make sure it works...

 

156 was the total before 2/3 (1/3)+(1/3) 

                                           52+52 = 104

were reduced leaving 52.

 

156-104=52 Problem solved 

Answer 2

2/3 n = 52 where n is the original number

 

n = 52 ÷ 2/3 (divide both sides by 2/3)

n = 52 x 3/2 (dividing by a fraction means multiplying by its inverse)

n = 52 x 3/2

n = 156/2

n = 78