Question

For your vegetable garden, you plan to plant 5 12 of it in corn, 1 6 in different kinds of beans, and 1 12 in tomatoes. You will plant the remainder equally in eggplant, onions, and squash. What part of the garden will be planted in onions and squash combined

Answer 1

`(1)/(9)`

Explanation:

Given:

Total fraction of garden for vegetation =
`(5)/(12)`

Fraction of beans =
`(1)/(6)`

Fraction of tomatoes =
`(1)/(12)`

It will plant the remainder equally in eggplant, onions, and squash.

Question asked:

What part of the garden will be planted in onions and squash combined ?

Solution:

Total fraction of garden for vegetation =

Fraction of beans =

Fraction of tomatoes =
`(1)/(12)`

Remaining fraction of garden =
`(5)/(12)-((1)/(6) +(1)/(12) )`

=
`(5)/(12) -(1)/(6) -(1)/(12)`

Taking LCM of 12, 6 and 12 =
`(5-2-1)/(12) =(2)/(12) =(1)/(6)`

Now, Remaining fraction for plant will be divided equally among eggplant, onions, and squash.

`(1)/(6) /3\\(1)/(6)*(1)/(3) =(1)/(18)`

Now, to find the combined fraction of onions and squash we will add both of the fraction.

Fraction of onions =
`(1)/(18)`

Fraction of squash =
`(1)/(18)`

combined fraction of onions and squash =
`(1)/(18)+(1)/(18)`

=
`(1+1)/(18) =(2)/(18) = (1)/(9)`

Therefore,
`(1)/(9)` part of the garden will be planted in onions and squash combined.

Answer 2

`(2)/(9)` part of the garden will be planted in onions and squash combined.

Explanation:

Given:

For your vegetable garden, you plan to plant 5 12 of it in corn, 1 6 in different kinds of beans, and 1 12 in tomatoes.

You will plant the remainder equally in eggplant, onions, and squash.

Now, to find the part of garden that will be planted in onions and squash combined.

Part of garden plan for planting corn =
`(5)/(12)`

Part of garden plan for planting kinds of bean =
`(1)/(6)`

Part of garden plan for planting tomatoes =
`(1)/(12)`

So, adding all the parts of corn, beans and tomatoes:

`(5)/(12)+(1)/(6) +(1)/(12) \\\\=(5+2+1)/(12) \\\\=(8)/(12)`

Now, to get the rest of the parts of garden use to plant eggplant, onions, and squash we subtract
`(8)/(12)` from 1 whole:

`1-(8)/(12) \\\\=(12-8)/(12) \\\\=(4)/(12)`

As, given planting the remainder equally in eggplant, onions, and squash.

So, each will be planted in part of:

`(4)/(12) / 3`

`=(4)/(12)* (1)/(3)`

`=(4)/(36)`

On simplifying it:

`=(1)/(9)`.

Thus,
`(1)/(9)` part of the garden for each eggplant, onions, and squash.

Now, to get the part of the garden will be planted in onions and squash combined we add
`(1)/(9)` part of garden planting for onions and
`(1)/(9)` of squash:

`(1)/(9) +(1)/(9) \\\\=(1+1)/(9) \\\\=(2)/(9)`

Therefore,
`(2)/(9)` part of the garden will be planted in onions and squash combined.