Question

1. an ice - skating rink charges $4 per hour to skate on the rink and the option to rent skates for an additional cost. marlo paid $13 to rent ice skates and to skate for two - and - a - half hours.

a. what is the cost of renting skates?
b. how much would it cost to rent skates and be on the ice for 4 hours?

1. niko drinks his shake at a constant rate. after drinking the shake for 3 minutes, there are 14 oz of shake left in the cup. after 9 minutes, the cup is empty.

a. graph the relationship between the time in minutes, and the ounces of shake left in his cup.
b. write an equation for s, the ounces of shake left in the cup, after t minutes.
c. identify the x and y intercepts and explain their meaning in the context of the problem.

Explanation:

1.

a.

Step1: Calculate skating cost

The cost per - hour for skating is $4, and Marlo skated for 2.5 hours. So the skating cost is $4\times2.5 = 10$.

Step2: Find skate - renting cost

Marlo paid a total of $13. Let the cost of renting skates be $x$. We know that the total cost is the sum of the skating cost and the skate - renting cost. So $x+10 = 13$. Solving for $x$, we get $x=13 - 10=3$.

Step1: Calculate 4 - hour skating cost

The cost per hour for skating is $4, and for 4 hours, the skating cost is $4\times4 = 16$.

Step2: Add skate - renting cost

We found that the cost of renting skates is $3. So the total cost of renting skates and skating for 4 hours is $16 + 3=19$.

Step1: Calculate the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(3,14)$ and $(x_2,y_2)=(9,0)$. So $m=\frac{0 - 14}{9 - 3}=\frac{-14}{6}=-\frac{7}{3}$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(9,0)$ and $m =-\frac{7}{3}$, we have $s-0=-\frac{7}{3}(t - 9)$. Simplifying, we get $s=-\frac{7}{3}t+21$.

Answer:

$3$

b.