Jaheem always helps his mother look after her fruit stall. At the fruit stall, 3 7 of the fruits are mangos. 3 8 of the remaining fruits are

Jaheem always helps his mother look after her fruit stall. At the fruit stall, 3/7 the fruits are mangos. 3/8 of the remaining fruits are kiwis and the rest are bananas. How many fruits are there altogether if there are 130 bananas?

Let the number of fruit be F

There are (3/7)F mangoes so there are   (4/7)F that are not mangos

There are (3/8)*(4/7)F   that are kiwi fruit

the rest are bananas

so

The number of bananas = total - mangos - kiwi fruit

The number of bananas = F -  (3/7)F  - (3/8)*(4/7)F    but there are 130 bananas

so

F -  (3/7)F  - (3/8)*(4/7)F = 130

F [ 1-  (3/7)  - (3/8)*(4/7)] =130

F=130 / [ 1-  (3/7)  - (3/8)*(4/7)]

$${\frac{{\mathtt{130}}}{\left[{\mathtt{1}}{\mathtt{\,-\,}}\left({\frac{{\mathtt{3}}}{{\mathtt{7}}}}\right){\mathtt{\,-\,}}\left({\frac{{\mathtt{3}}}{{\mathtt{8}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{4}}}{{\mathtt{7}}}}\right)\right]}} = {\mathtt{364}}$$

So ther are 364 peices of fruit