Question

accelerated 6 unit 4 section d checkpoint

1. tyler bought 4 ounces of vegetable seeds for $19 from an online store that sells seeds in bulk.

a. complete the table to show the costs for different amounts of seeds.

b. write an equation that shows the relationship between the weight of seeds in ounces, w, and the cost in dollars, c.

weight of seeds (ounces)	4	10	50

Explanation:

Part a: Completing the Table

Step 1: Find the unit rate (cost per ounce)

We know that 4 ounces cost $19. So the unit rate (cost per ounce) is calculated by dividing the cost by the weight. Let's find the cost per ounce first. The cost for 4 ounces is $19, so the cost per ounce \( r = \frac{19}{4}= 4.75 \) dollars per ounce.

Step 2: Calculate cost for 10 ounces

To find the cost for 10 ounces, we multiply the unit rate by 10. So cost \( c = 4.75\times10 = 47.5 \) dollars.

Step 3: Calculate cost for 50 ounces

To find the cost for 50 ounces, we multiply the unit rate by 50. So cost \( c = 4.75\times50 = 237.5 \) dollars.

Now we can complete the table:

weight of seeds (ounces)	4	10	50

Part b: Writing the Equation

Step 1: Identify the relationship type

The relationship between weight (\( w \)) and cost (\( c \)) is a proportional relationship because the cost per ounce is constant (we found the unit rate in part a). In a proportional relationship, the equation is of the form \( c = r\times w \), where \( r \) is the unit rate (constant of proportionality).

Step 2: Determine the constant of proportionality

From part a, we found that the unit rate (cost per ounce) \( r=\frac{19}{4} = 4.75 \) dollars per ounce.

Step 3: Write the equation

Using the proportional relationship formula \( c = rw \), substituting \( r = 4.75 \) (or \( \frac{19}{4} \)), we get the equation \( c = 4.75w \) (or \( c=\frac{19}{4}w \)).

Final Answers:

Part a:

The completed table is:

weight of seeds (ounces)	4	10	50

Part b:

The equation is \( \boldsymbol{c = 4.75w} \) (or \( \boldsymbol{c=\frac{19}{4}w} \))

Answer:

Step 1: Identify the relationship type

The relationship between weight (\( w \)) and cost (\( c \)) is a proportional relationship because the cost per ounce is constant (we found the unit rate in part a). In a proportional relationship, the equation is of the form \( c = r\times w \), where \( r \) is the unit rate (constant of proportionality).

Step 2: Determine the constant of proportionality

From part a, we found that the unit rate (cost per ounce) \( r=\frac{19}{4} = 4.75 \) dollars per ounce.

Step 3: Write the equation

Using the proportional relationship formula \( c = rw \), substituting \( r = 4.75 \) (or \( \frac{19}{4} \)), we get the equation \( c = 4.75w \) (or \( c=\frac{19}{4}w \)).

Final Answers:

Part a:

The completed table is:

weight of seeds (ounces)	4	10	50

Part b:

The equation is \( \boldsymbol{c = 4.75w} \) (or \( \boldsymbol{c=\frac{19}{4}w} \))