For the stated word problem, we need to use variable to represent the unknown counts per each fruit. We may let:
o = original number of oranges
a= original number of apples
p = original number of pears.
To set-up an equation, we translate the given conditions in the problem.
Condition 1: A fruiterer had the same number of apples, pears and oranges at first.
This implies that we can equate them as `o =a=p` .
Condition 2:After 98 oranges, some apples and pears were sold, there were 392 fruits left.
We may let:
unsold oranges = o'
unsold apples = a'
unsold pears = p'
It indicates that the sum of the remaining number of fruits = 392 such that: sold oranges =98
`o' +a' +p' = 392`
Condition 3: There were thrice as many apples as pears left
This means that `a' =3p'` or `p' =(a')/3`
Condition 4: The number of oranges left was 35 fewer than the number of apples left.
`o' = a' -35 `
Using ` a'=3p'` , we get: `o'=3p'-35`
Applying condition 3: `a' = 3p'` and condition 4: `o' = 3p'-35` on condition 2:
`3p'-35 +3p' +p' = 392`
p'=61 as the number of "unsold pears".
Plug-in `p' =61` on `o'=3p'-35` , we get:
`o' = 3(61)-35`
`o' =148` as number of unsold oranges
With sold oranges = 98 and unsold oranges=148 then
original number of oranges: `o= 246` .
Applying ` o=a=p` , we can determine that we also have:
246 original number of pears and 61 unsold pears.
sold pears: `246-61 =185` [FINAL ANSWER]
In addition, the other unsold apples and oranges are:
Plug-in `p' =61` on `a'=3p'` , we get:
`a'=3*61=183` as number of unsold apples
then sold apples: `246-83=63`
Here is the tally.
Number of sold fruits: 63 apples, 185 pears, and 98 oranges
Number of unsold fruits: 183 apples, 61 pears, and 148 oranges