Question

Sally had some stickers. She lost 2/3 of them and gave 1/4 of the remainder to Paul. After that, her brother gave her 120 stickers. The ration of the number of stickers she had at first to the number of stickers she had in the end was 4:3. Hhow many stickers did Sally have in the end?

Answer 1

This is the concept of algebra, To get the total number of stickers Sally had in the end we proceed as follows;
Suppose the initial number of stickers was x;
When she lost 2/3 of the tickets the remaining, the number of tickets that she lost was 2/3x.
The remaining number of tickets will be:
x-2/3x=1/3x
The number of tickets she gave to Paul will be given by:
1/3x*1/4
1/12x
After her brother gave her 120 tickets, the new number of tickets was:
1/12x+120
=(x+1440)/12
The ratio of the original number to the number she ended up with is 4:3, therefore;
x/[(x+1440)/12]=4/3
x*12/[x+1140]=4/3
[12x]/[x+1440]=4/3
cross-multiplying the expression we get:
3*12x=4[x+1440]
36x=4x+5760
32x=5760
dividing both sides by 32 we get:
(32x)/32=5760/32
x=180
Therefore the initial number of tickets was 180 tickets