Question

At the beginning of the season, MacDonald had to remove 5 orange trees from his farm. Each of the remaining trees produced 210 oranges for a total harvest of 41790 oranges.

Equations
and
Answer

Answer 1

Equations: f(t) = 210(t-5)

Initial number of trees(t) = 204

Explanation:

Let t represents the initial number of trees and f(t) represents the total number of oranges.

"Remove 5 orange trees from his farm" means (t-5)

" Each of the remaining trees produced 210 oranges" means
`210\cdot (t-5)`

so, the equation become
`f(t) = 210 \cdot (t-5)`

Also, it is given that total harvest of, 41790 oranges.

⇒f(t) = 41790

Substitute this in the above equation to get t;

`41790 = 210(t-5)`

Divide both sides by 210 we get;

`199 = t-5`

Add 5 both sides of an equation we get;

199 + 5 = t-5 + 5

Simplify:

204 = t

Therefore, there were initially 204 orange trees

Answer 2

Let t = initial number of trees "remove 5 trees at the start of the season"  means     (t    - 5)     remain "each remaining tree made 210 oranges for a total of 41,790 oranges"    means         ( t   - 5)           *        210                  = 41790 Now, you can solve for t:        (t-5)(210) = 41790                     [just re-writing]        210t - 1050 = 41790                    [distribute]        210t = 42840                            [add 1050 to each side]          t = 204                                  [divide each side by 210] There were initially 204 trees.  After 5 were removed, the remaining 199 produced 210 oranges each for a total of 199*210 = 41790 oranges.