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

Answer:

D. between 3/4 and 1 full pitcher

Step-by-step 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

$\frac{3}{4} x = \frac{2}{3}$

$x = \frac{2*4}{3*3}$

$x = \frac{8}{9}$

$x =0.88$

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

Answer 2

Answer:

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

Step-by-step explanation:

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

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