Question

Jan is planting tomatp plants in her garen last year she planted 24 plants and harvested 12 bushels pf tomatoes during the seson this year she has decided to only plant 18 plants if the number of the plants dirctly proportional to the number of bushels of tomatoes harvested how many bushels of tomatoes should she expect this year

Answer 1

Jan should expect 9 bushels of tomatoes this year

Solution:

Given that,

The number of the plants directly proportional to the number of bushels of tomatoes harvested

Let "y" be the number of plants

Let "x" be number of bushels of tomatoes harvested

Then,

`y \propto x`

y = kx -------- eqn 1

where, k is constant

Last year she planted 24 plants and harvested 12 bushels of tomatoes

Substitute y = 24 and x = 12 in eqn 1

`24 = k * 12\\\\k = (24)/(12)\\\\k = 2`

During the season this year she has decided to only plant 18 plants

Plug in y = 18, k = 2 in eqn 1

`18 = 2 * x\\\\x = 9`

Thus, he should expect 9 bushels of tomatoes this year