Question 493029
Let x = the total number of crates of the entire orange crop.
The number of crates of oranges destoyed by frost = {{{(1/5)x}}} thus leaving a remainder of {{{x-(1/5)x = (4/5)x}}} crates to be processed into orange juice.
But one half of this remainder was sent to be processed into orange juice and this amounted to 1600 crates.
Setting up the equation in terms of x, we get:
{{{(1/2)(4/5)x = 1600}}}
{{{(4/10)x = 1600}}} Multiply both sides by the multiplicative inverse of {{{4/10}}} which is {{{10/4}}} we get:
{{{x = (10/4)(1600)}}}
{{{x = 4000}}}crates in the total orange crop.
One fifth of this total was destroyed by frost, so...
{{{(1/5)(4000) = 800}}}crates.
800 crates of oranges were destroyed by frost.