Question

practice & problem solving
leveled practice for 6 and 7, complete the information to compare the rates.

1. sam and bobby want to know who cycled faster. the table shows the total miles sam traveled over time. the graph shows the same relationship for bobby. who cycled faster?

find the unit rate (constant of proportionality) for sam.
distance/time = 20/2 = (\frac{miles}{hour})
find the unit rate (constant of proportionality) for bobby.
use ( , ) and ( , ) to find the constant of proportionality.
the unit rate (constant of proportionality) is (\frac{miles}{hour})
so cycled faster.

1. model with math the equation y = 15x can be used to determine the amount of money, y, paulis pizzeria makes by selling x pizzas. the graph shows the money leos pizzeria takes in for different numbers of pizzas sold. which pizzeria makes more money per pizza?

paulis pizzeria takes in per pizza.
leos pizzeria takes in per pizza.
s pizzeria takes in more money per pizza.

1. the graph shows the amount of savings over time in elianas account. lana, meanwhile, puts $50 each week into her savings account. if they both begin with $0, who is saving at the greater rate?

Explanation:

Step1: Calculate Sam's unit rate

$\frac{20}{2}=10$ miles per hour

Step2: Select points for Bobby

Choose (2, 18) and (4, 36) on Bobby's graph

Step3: Calculate Bobby's unit rate

$\frac{36 - 18}{4 - 2}=\frac{18}{2}=9$ miles per hour

Step4: Compare rates

Since $10>9$, Sam cycled faster

Step1: Find Pauli's rate

For Pauli's Pizzeria, from $y = 15x$, the rate is 15 dollars per pizza

Step2: Find Leo's rate

From Leo's graph, if $x = 2,y=24$, then $\frac{24}{2}=12$ dollars per pizza

Step3: Compare rates

Since $15>12$, Pauli's Pizzeria takes in more money per pizza

Step1: Find Eliana's rate

From Eliana's graph, if $x = 2,y = 94$, and starting with $y(0)=0$, rate $=\frac{94}{2}=47$ dollars per week

Step2: Compare rates

Lana saves 50 dollars per week. Since $50>47$, Lana is saving at a greater rate

Answer:

for Question 6:

• Sam's unit - rate: 10 miles per hour
• For Bobby, use points (2, 18) and (4, 36) (any two points on the line). The unit rate (constant of proportionality) is 9 miles per hour. Sam cycled faster.