at the deli counter in the supermarket, Nigel paid $10 for 2 1/2 pounds of roast beef. the cost of deli meat is proportional to its weight. what is the equation for the graph of this proportional relationship?
Let x represent the weight of the deli meat in pounds and y represent the cost of the deli meat in dollars.
Since the cost of deli meat is proportional to its weight, we can write the equation as follows:
y = kx, where k is the constant of proportionality.
To find the value of k, we can use the given information that Nigel paid $10 for 2 1/2 pounds of roast beef.
So, when x = 2.5, y = 10.
Substituting these values into the equation, we have:
10 = k(2.5)
Divide both sides of the equation by 2.5:
10/2.5 = k
4 = k
Therefore, the equation for the graph of this proportional relationship is:
y = 4x.
At the Custard Creamery, the cost of ice cream custard is directly proportional to its weight in ounces. Complete the equation of the graph with its constant of proportionality. (1 point)
Let x represent the weight of the ice cream custard in ounces and y represent the cost of the ice cream custard in dollars.
Since the cost of ice cream custard is directly proportional to its weight, we can write the equation as follows:
y = kx, where k is the constant of proportionality.
To find the value of k, we need more information about the specific values of x and y.
If we are given that the cost of 10 ounces of ice cream custard is $5, we can substitute these values into the equation:
5 = k(10)
Divide both sides of the equation by 10:
5/10 = k
1/2 = k
Therefore, the complete equation for the graph of this proportional relationship is:
y = (1/2)x.
The age of a dog is proportional to the age of a human. Based on the graph, determine a dog’s age if a human is 3 years old. (1 point)
To determine a dog's age based on the graph if a human is 3 years old, we need to determine the constant of proportionality between the age of a dog and the age of a human.
Let's assume that x represents the age of a human and y represents the age of a dog.
From the graph, we can determine two points: (1, 7) and (5, 35).
Using these points, we can find the constant of proportionality, k.
The equation for the proportional relationship is y = kx.
Substituting the values from the first point into the equation, we get:
7 = k(1)
Solving for k, we find that k = 7.
Now, using the constant of proportionality, we can find the age of a dog when a human is 3 years old.
Substituting x = 3 and k = 7 into the equation y = kx, we have:
y = 7(3)
y = 21
Therefore, based on the graph, a dog's age would be 21 years if a human is 3 years old.
Trisha's mom asked her to fill up the car's gas tank and gave her $30. The graph shows the total cost of gas based on the number of gallons. The point X shows the number of gallons of gasoline Trisha can purchase. State, to the nearest whole, the number of gallons of gasoline she can purchase.
Without the graph or specific data points, it is not possible for me to directly state the number of gallons of gasoline Trisha can purchase. However, given that Trisha has $30 and the graph shows the total cost of gas based on the number of gallons, we can make an estimation by looking at the graph.
To estimate the number of gallons of gasoline Trisha can purchase, we need to find the corresponding point on the graph where the cost of gas is closest to $30.
Using the graph, locate the point where the graph intersects with the $30 price line. The x-coordinate of this point on the graph represents the estimated number of gallons of gasoline Trisha can purchase.
For example, if the graph shows that the cost of gas is $30 for 8 gallons, then the estimated number of gallons of gasoline Trisha can purchase is approximately 8.
Therefore, to the nearest whole number, the number of gallons of gasoline Trisha can purchase would be the x-coordinate of the intersection point on the graph closest to the $30 price line.
Miley is saving for a new pair of boots. They cost $150. Every week, she puts $25 into her savings account. Based on the graph, state the number of weeks it will take for her to save enough money to buy the boots.
To determine the number of weeks it will take for Miley to save enough money to buy the boots, we need to examine the graph or have more specific information about the savings progress displayed on the graph.
Without the graph or more specific information, we cannot directly state the number of weeks it will take for Miley to save enough money. However, we can use the given information to calculate an estimate.
If Miley saves $25 every week and the boots cost $150, we can divide the cost of the boots by the weekly savings amount to get an estimate of the number of weeks it will take.
Dividing $150 by $25, we find that it will take Miley approximately 6 weeks to save enough money to buy the boots.
Therefore, based on the given information, it will take Miley around 6 weeks to save enough money to buy the boots.
To find the equation for the graph of the proportional relationship between the cost of deli meat and its weight, we need to determine the constant of proportionality.
In this case, we know that Nigel paid $10 for 2 1/2 pounds of roast beef. We can represent this information as a ratio or fraction:
Cost/Weight = $10 / 2.5 pounds.
To find the constant of proportionality, we can simplify this ratio by dividing both the numerator and the denominator by the same number until we get a whole number. Let's simplify the fraction by dividing both sides by 2.5:
Cost/Weight = $10 / 2.5 pounds
= $4 / 1 pound.
Now we have a simplified ratio of cost to weight: $4 for every 1 pound of deli meat.
Since the cost of deli meat is proportional to its weight, we can represent this proportional relationship using an equation. Let's use "C" to represent the cost of deli meat and "W" to represent its weight. Therefore, the equation that represents the graph of this proportional relationship is:
C = 4W.
Here, "C" represents the cost in dollars, and "W" represents the weight in pounds. This equation shows that the cost of the deli meat is four times its weight.