Question

Alana will use a 3/4 gallon pitcher to fill an empty 2/3 gallon bucket. How much water will she need to completely fill the bucket?

A) between 1 and 2 full pitchers

B) between 0 and 1/4 of a pitcher

C) about 1/2 of a pitcher

D) between 3/4 and 1 full pitcher

Answer 1

The correct option is A. Between 1 and 2 full pitchers

Explanation:

`\text{Water needed to fill }(2)/(3)\text{ gallon bucket = }(3)/(4)\text{ gallons of water in pitcher}\\\\\text{Now, to find the amount of water in pitcher needed to fill one full empty bucket}\\\text{we divide the amount of water in pitcher needed to fill }(2)/(3)\text{ gallon of bucket by }(2)/(3)\\\\\implies\text{Water needed by Alana to completely fill the bucket = }((3)/(4))/((2)/(3))\\\\\implies (3)/(4)* (3)/(2)=(9)/(8)\\\\\textbf{Hence, Amount of water needed to fill bucket completely = }\bf(9)/(8)`

So, The correct option is A. Between 1 and 2 full pitchers

Answer 2

D. between 3/4 and 1 full pitcher

Explanation:

Given : Alana will use a 3/4 gallon pitcher to fill an empty 2/3 gallon bucket

To Find: How much water will she need to completely fill the bucket?

Solution :

let x be the water she will need to completely fill the bucket

Since we are given that Alana will use a 3/4 gallon pitcher to fill an empty 2/3 gallon bucket

Since

`(3)/(4) x = (2)/(3)`

`x = (2*4)/(3*3)`

`x = (8)/(9)`

`x =0.88`

So, she will need between 3/4(0.75) and 1 full pitcher need to completely fill the bucket