A farmer, Jenni, grows oranges and grapefruit. At her last harvest she picked 120120 grapefruit and a number of oranges. However, one-tenth of all grapefruit look like oranges and one-tenth of all oranges look like grapefruit. Overall, one-fifth of all fruits look like grapefruit.How many oranges did Jenni harvest?

Let's denote the number of oranges that Jenni harvested as O.

According to the problem, one-tenth of all grapefruit look like oranges and one-tenth of all oranges look like grapefruit. This means that there are 0.1120120 = 12012 grapefruit that look like oranges and 0.1O oranges that look like grapefruit.

The problem also states that overall, one-fifth of all fruits look like grapefruit. This means that the number of fruits that look like grapefruit is equal to one-fifth of the total number of fruits. The total number of fruits is the sum of the number of grapefruit and the number of oranges, which is 120120 + O.

So, we can write the equation:

0.1O + (120120 - 12012) = 0.2(120120 + O)

Solving this equation for O gives us the number of oranges that Jenni harvested.

First, simplify the equation:

0.1O + 108108 = 24024 + 0.2O

Then, subtract 0.1*O from both sides:

108108 = 24024 + 0.1*O

Subtract 24024 from both sides:

83984 = 0.1*O

Finally, divide both sides by 0.1 to solve for O:

O = 839840

So, Jenni harvested 839840 oranges.

Let's denote the number of oranges that Jenni harvested as O.

According to the problem, one-tenth of all grapefruit look like oranges and one-tenth of all oranges look like grapefruit. This means that the number of fruits that look like grapefruit is the sum of the actual grape