Question

1. jack, jill, and bill each carried a 48-ounce bucket full of water down the hill. by the time they bottom, jacks bucket was only \\( \frac{3}{4} \\) full, jills was \\( \frac{2}{3} \\) full, and bills was \\( \frac{1}{6} \\) full. how much water did they spill altogether on their way down the hill? draw a pictorial model to show your thinking.\

\\( 48 \times \frac{3}{4} = 36 \\) \\( 48 - 36 = 12 \\)\
\\( 48 \times \frac{2}{3} = 32 \\) \\( 48 - 32 = 16 \\)\
\\( 48 \times \frac{1}{6} = 8 \\) \\( 48 - 8 = 40 \\)\
\\( 12 + 16 + 40 = 68 \\)\
\

1. mrs. diaz makes 5 dozen cookies for her class. one-ninth of her 27 students are absent the day she brings the cookies. if she shares the cookies equally among the students who are present, how many cookies will each student get? draw a pictorial model to show your thinking.

Explanation:

Problem 3:

Step 1: Calculate spilled by Jack

Jack's bucket was \( \frac{3}{4} \) full, so spilled is \( 48\times(1 - \frac{3}{4}) = 48\times\frac{1}{4}=12 \) ounces.

Step 2: Calculate spilled by Jill

Jill's bucket was \( \frac{2}{3} \) full, so spilled is \( 48\times(1 - \frac{2}{3}) = 48\times\frac{1}{3}=16 \) ounces.

Step 3: Calculate spilled by Bill

Bill's bucket was \( \frac{1}{6} \) full, so spilled is \( 48\times(1 - \frac{1}{6}) = 48\times\frac{5}{6}=40 \) ounces.

Step 4: Total spilled

Sum the spills: \( 12 + 16 + 40 = 68 \) ounces.

Step 1: Total cookies

5 dozen = \( 5\times12 = 60 \) cookies.

Step 2: Absent students

\( \frac{1}{9}\times27 = 3 \) students absent.

Step 3: Present students

\( 27 - 3 = 24 \) students present.

Step 4: Cookies per student

Divide total cookies by present students: \( \frac{60}{24} = 2.5 \) cookies.

Answer:

68 ounces

Problem 4: