How much more cabbages do he need?

Question

Matt is picking cabbages and putting them into a crate.At midday the crate is two-thirds full. But he added another 150 cabbages and now the crate is 7/8 full.How much more cabbages must he put into the crate to fill it comepletly?

Answer 1

How much did we add to 2/3 to reach 7/8?

 

2/3 + x = 7/8

x = 7/8 - 2/3

x = 21/24 - 16/24

x = 5/24

This 5/24 of the crate was taken up by 150 cabbages, i.e.,

150 cabbages fills 5/24 of the crate

 

There is 1/8 of the crate left to fill

1/8 = 3/24

3/24 = (3/5)(5/24)

 

This means we can use 3/5 of 150 cabbages to fill the crate

(3/5)(150) = 3(30) = 90 cabbages