SOLUTION: A shop had a number of T-shirts for sale. After selling 72 of them in the morning and 4/9 of the remainder in the afternoon, it was left with 1/3 of the T-shirts. How many T-shirts

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A shop had a number of T-shirts for sale. After selling 72 of them in the morning and 4/9 of the remainder in the afternoon, it was left with 1/3 of the T-shirts. How many T-shirts      Log On


   

Question 1184059: A shop had a number of T-shirts for sale. After selling 72 of them in the morning and 4/9 of the remainder in the afternoon, it was left with 1/3 of the T-shirts. How many T-shirts were sold altogether?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52802) About Me  (Show Source):
You can put this solution on YOUR website!
.

    72 + %284%2F9%29%2A%28x-72%29 + x%2F3 = x.


You do the rest.


Your goal is to find x, the total number of the T-shirts.


To do it, multiply both sides by 9 and simplify.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the original number of t-shirts.

72 were sold, leaving (x-72)
4/9 of those (x-72) were then sold
1/3 of the original x remained

The total number sold, plus the number remaining, equals the original total:

72%2B%284%2F9%29%28x-72%29%2B%281%2F3%29x=x
72%2B%284%2F9%29x-32%2B%281%2F3%29x=x
40=x-%284%2F9%29x-%281%2F3%29x+=+%282%2F9%29x
x=180

The original number of t-shirts was 180
72 were sold, leaving 108
4/9 of those 108, or 48, were sold, leaving 60, which is 1/3 of the original number.

ANSWER: The total number sold was 72+48=120