Lauren is making muffins. Her muffin recipe calls for 3 1 −4 cups of flour. She has 10 1 −2 cups of flour. A. Explain a method for determining the number of batches of the muffin recipe Lauren can make. Then use your method to find the number of batches she can make. B. If Lauren plans to make 5 batches of the muffin recipe, use what you know about operating with rational numbers to predict the amount of flour she needs. Justify your prediction.

A. 3.2307692308 batches of Muffins

B. 16 1/4 cups of flour

Step-by-step explanation:

Lauren is making muffins. Her muffin recipe calls for 3 1 −4 cups of flour. She has 10 1 −2 cups of flour.

A. Explain a method for determining the number of batches of the muffin recipe Lauren can make. Then use your method to find the number of batches she can make.

Her muffin recipe calls for 3 1 −4 cups of flour. She has 10 1 −2 cups of flour.

3 1/4 cups of flour = 1 batch of Muffin recipe

10 1/2 cups of flour = x

3 1/4 × x = 10 1/2 × 1

x = 10 1/2 ÷ 3 1/4

x = 21/2 ÷ 13/4

x = 21/2 × 4/13

x = 42/13

x = 3.2307692308 batches of Muffins

B. If Lauren plans to make 5 batches of the muffin recipe, use what you know about operating with rational numbers to predict the amount of flour she needs. Justify your prediction.

3 1/4 cups of flour = 1 batch of Muffin recipe

Hence,

1 batch = 3 1/4 cups of flour

5 batches = x

Cross Multiply

x = 5 × 3 1/4 cups of flour

x = 5 × 13/4

x = 65/4

x = 16 1/4 cups of flour

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.

72 is the answer to this problem