Question

1. mr. bobs grandchildren are helping him mow his field. each one mows at a different rate. drag each persons mowing rate on the left to the equivalent unit rate on the right. allison mows $\frac{1}{3}$ acre in $\frac{1}{6}$ hour. betty mows $\frac{5}{12}$ acre in $\frac{5}{6}$ hour. clyde mows $\frac{3}{5}$ acre in $\frac{3}{10}$ hour. debra mows $\frac{2}{9}$ acre in $\frac{4}{9}$ hour. 6. based on the graph of hot dog sales, which coordinate point represents the cost of 38 hot dogs? a. (19, 38) b. (38, 19) c. (38, 76) d. (76, 38) the graph shows hot dog sales during the tournament. 7. the following statements refer to the graph of hot dog sales. determine whether each statement is true or false. the ordered pair (0, 0) represents no hot dogs purchased and no money spent. the ordered pair (1, 2) represents 2 hot dogs purchased for $1. the ordered pair (20, 10) represents $20 spent for 10 hot dogs. the ordered pair (45, 90) represents $45 spent for 90 hot dogs.

Explanation:

Step1: Calculate Allison's mowing rate

To find the unit - rate, divide the number of acres by the number of hours. For Allison, $\frac{\frac{1}{3}}{\frac{1}{6}}=\frac{1}{3}\times\frac{6}{1}=2$ acres per hour.

Step2: Calculate Betty's mowing rate

For Betty, $\frac{\frac{5}{12}}{\frac{5}{6}}=\frac{5}{12}\times\frac{6}{5}=\frac{1}{2}$ acre per hour.

Step3: Calculate Clyde's mowing rate

For Clyde, $\frac{\frac{3}{5}}{\frac{3}{10}}=\frac{3}{5}\times\frac{10}{3}=2$ acres per hour.

Step4: Calculate Debra's mowing rate

For Debra, $\frac{\frac{2}{9}}{\frac{4}{9}}=\frac{2}{9}\times\frac{9}{4}=\frac{1}{2}$ acre per hour.

Step5: Solve question 6

From the graph, if the number of hot - dogs is on the x - axis and the cost is on the y - axis, when the number of hot - dogs $x = 38$, looking at the graph, the corresponding cost $y=76$. So the coordinate point is $(38,76)$.

Step6: Solve question 7

• For the ordered pair $(0,0)$: When $x = 0$ (number of hot - dogs) and $y = 0$ (cost), it means no hot - dogs purchased and no money spent. So this statement is True.
• For the ordered pair $(1,2)$: It means 1 hot - dog purchased for $2$. So the statement "2 hot - dogs purchased for $1$" is False.
• For the ordered pair $(20,10)$: It means 20 hot - dogs purchased for $10$, not $20$ spent for 10 hot - dogs. So this statement is False.
• For the ordered pair $(45,90)$: It means 45 hot - dogs purchased for $90$, not $45$ spent for 90 hot - dogs. So this statement is False.

Answer:

1. Allison: 2 acres per hour; Betty: $\frac{1}{2}$ acre per hour; Clyde: 2 acres per hour; Debra: $\frac{1}{2}$ acre per hour
2. C. $(38,76)$

7.

Statement	True	False
The ordered pair $(1,2)$ represents 2 hot dogs purchased for $1$.		$\bigcirc$
The ordered pair $(20,10)$ represents $20$ spent for 10 hot dogs.		$\bigcirc$
The ordered pair $(45,90)$ represents $45$ spent for 90 hot dogs.		$\bigcirc$