Question too long pls look at desc

Question

85% of the fruits in a basket wereapples and the rest were mangoes. When 141 more apples and mangoes were added to the basket the percentage of apples increased by 20% and the numbers of mangoes tripled. How many apples are there in the basket at first

Answer 1

After careful reading, we determine that there are just two variables for which we must solve:

    x = the number of apples at first

    y = the number of mangoes at first

 

Note: the basket contains only apples and mangoes, so (x+y) = total number of fruits at first

 

Translate:

"85% of the fruits in a basket were apples"     means    x = (85/100)(x+y)        [eq1]

    [note: 85% may be written as (85/100) or 0.85 as needed by the problem]

 

"the rest were mangoes"    means   y = (15/100)(x+y)             [eq2]

 

"141 more apples and mangoes were added "   means

     new total number in the basket is now  (x+y+141)

 

"percentage of apples increased by 20%"   and

"numbers of mangoes tripled"        means

    new number of apples   +   new number of mangoes    = new total

   (120/100)x                   +         3y                               =  (x+y+141)     [eq3]

 

    (x+y) = (100/85)x             [from eq1]

       y = (100/85)x - x

       y = (100/85)x - (85/85)x

       y = ((100-85)/85)x

       y = (15/85)x

       y = (3/17)x      [eq4]

 

   (120/100)x   + 3(3/17)x  =    x  +  (3/17)x  +  141    [substitute into eq3]

     2040x        +   900x      = 1700x +  300x   +  239700   [multiply by 1700 to get rid of fractions]

        940x = 239700

           x = 255

 

There were 255 apples in the basket at first.

 

Check:

   There were (3/17)255 = 45 mangoes at first.     [use eq4]

   At the end, there were (120/100)(255) = 306 apples.

   At the end there were (3*45) = 135 mangoes.

   That's (306-255) + (135-45) = 51 + 90 = 141 more apples and mangoes;   CHECK!