i need help again 100 pts

Answer:

1. Becky's rate of sales is 9 cups per hour

2. Mayisha's rate of sales is 10 cups per hour

3. Becky is selling 1 fewer cups per hour than Mayisha

4. Becky started with 2 fewer cups than Mayisha

Step-by-step explanation:

1. 30-12=18 18/2=9

2. 31-21=10 21-11=10

3. 10-9=1

4. 30+9=39 31+10=41 41-39=2

Answer:

Becky's rate of sales is [tex]\boxed{\sf 9}[/tex] cups per hour.

Mayisha's rate of sales is [tex]\boxed{\sf 10}[/tex] cups per hour.

Becky is selling [tex]\boxed{\sf 1\: fewer}[/tex] cup(s) per hour than Mayisha.

Becky started with [tex]\boxed{\sf 2}[/tex] fewer cups than Mayisha.

Step-by-step explanation:

Mayisha

[tex]\begin{array}{|c|c|c|c|}\cline{1-4} \sf Hours\:(x) & 1 & 2 & 3\\\cline{1-4} \sf Cups\: {left}\:(y) & 31 & 21 & 11\\\cline{1-4} \end{array}[/tex]

Becky

[tex]\begin{array}{|c|c|c|c|}\cline{1-4} \sf Hours\:(x) & 1 & 2 & 3\\\cline{1-4} \sf Cups\: {left}\:(y) & 30 & & 12\\\cline{1-4} \end{array}[/tex]

Selling at a steady rate.

To calculate the rate of sales, use the rate of change formula:

[tex]\sf Rate\:of\:change = \dfrac{change\:in\:y}{change\:in\:x}[/tex]

Therefore:

[tex]\textsf{Becky's rate of sales}=\dfrac{12-30}{3-1}=-9[/tex]

Therefore, as the number of cups reduces by 9 each hour, Becky's rate of sales is 9 cups per hour.

[tex]\textsf{Mayisha's rate of sales}=\dfrac{11-31}{3-1}=-10[/tex]

Therefore, as the number of cups reduces by 10 each hour, Mayisha's rate of sales is 10 cups per hour.

As 9 is one less than 10, Becky is selling 1 fewer cup(s) per hour than Mayisha.

As Becky had 30 cups left after 1 hour, and her rate of sales is 9 cups, then she started with 30 + 9 = 39 cups.

As Mayisha had 31 cups left after 1 hour, and her rate of sales is 10 cups, then she started with 31 + 10 = 41 cups.

As 39 is 2 less than 41, Becky started with 2 fewer cups than Mayisha.

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