Question

!QUICK! Garrett needs 3 gallons of fruit juice to make punch.

He already has 5/6 gallon of grape juice and 2/3 gallon of orange juice.

Drag amounts of juice that he can add to the juice he already has to make exactly 3 gallons

The Choices are 1/3 Gal and 1/6 Gal

Answer 1

`(1)/(6)` gallon

Explanation:

Quantity of fruit juice needed by Garrett = 3 gallons

Quantity of grape juice with Garrett =
`(5)/(6)` gallon

Quantity of orange juice with Garrett =
`(2)/(3)` gallon

We need to find quantity of juice he can add to the juice he already has to make exactly 3 gallons of juice.

Quantity of juice he can add to the juice he already has to make exactly 3 gallons of juice =
`3-(5)/(6)-(2)/(3)`

Here , LCM ( 3 , 6 ) = 6

So,

`3-(5)/(6)-(2)/(3)\\=(18-5-12)/(6)`

On solving terms in numerator , we get
`18-5-12=1`

Therefore ,

Quantity of juice he can add to the juice he already has to make exactly 3 gallons of juice =
`(1)/(6)` gallon .